Ronald Graham Information (Person)
Ronald Graham  

Born  Ronald Lewis Graham October 31, 1935
Taft, California, U.S. 
Died  July 6, 2020
San Diego, California, U.S.  (aged 84)
Alma mater 

Known for  
Spouse(s)  
Awards 

Scientific career  
Fields  
Institutions  
Thesis  On Finite Sums of Rational Numbers (1962) 
Doctoral advisor  Derrick Henry Lehmer 
Ronald Lewis Graham (October 31, 1935 – July 6, 2020)^{ [1]} was an American mathematician credited by the American Mathematical Society as "one of the principal architects of the rapid development worldwide of discrete mathematics in recent years".^{ [2]} He was president of both the American Mathematical Society and the Mathematical Association of America, and his honors included the Leroy P. Steele Prize for lifetime achievement and election to the National Academy of Sciences.
After graduate study at the University of California, Berkeley, Graham worked for many years at Bell Labs and later at the University of California, San Diego. He did important work in scheduling theory, computational geometry, Ramsey theory, and quasirandomness,^{ [3]} and many topics in mathematics are named after him. He published six books and about 400 papers, and had nearly 200 coauthors, including many collaborative works with his wife Fan Chung and with Paul Erdős.
Graham has been featured in Ripley's Believe It or Not! for being not only "one of the world's foremost mathematicians", but also an accomplished trampolinist and juggler. He served as president of the International Jugglers' Association.^{ [3]}^{ [4]}^{ [5]}
Biography
Graham was born in Taft, California, on October 31, 1935;^{ [6]} his father was an oil field worker and later merchant marine. Despite Graham's later interest in gymnastics, he was small and nonathletic.^{ [7]} He grew up moving frequently between California and Georgia, skipping several grades of school in these moves, and never staying at any one school longer than a year.^{ [1]}^{ [7]} As a teenager, he moved to Florida with his thendivorced mother, where he went to but did not finish high school. Instead, at the age of 15 he won a Ford Foundation scholarship to the University of Chicago, where he learned gymnastics but took no mathematics courses.^{ [1]}
After three years, when his scholarship expired, he moved to the University of California, Berkeley, officially as a student of electrical engineering but also studying number theory under Derrick Henry Lehmer,^{ [1]} and winning a title as California state trampoline champion.^{ [7]} He enlisted in the United States Air Force in 1955, when he reached the age of eligibility,^{ [8]} left Berkeley without a degree, and was stationed in Fairbanks, Alaska, where he finally completed a bachelor's degree in physics in 1959 at the University of Alaska Fairbanks.^{ [1]} Returning to the University of California, Berkeley for graduate study, he received his Ph.D. in mathematics in 1962. His dissertation, supervised by Lehmer, was On Finite Sums of Rational Numbers.^{ [9]} While a graduate student, he supported himself by performing on trampoline in a circus,^{ [8]} and married Nancy Young, an undergraduate mathematics student at Berkeley; they had two children.^{ [1]}
After completing his doctorate, Graham went to work in 1962 at Bell Labs and later as Director of Information Sciences at AT&T Labs, both in New Jersey. In 1963, at a conference in Colorado, he met the prolific Hungarian mathematician Paul Erdős (1913–1996),^{ [1]} who became a close friend and frequent research collaborator. Graham was chagrined to be beaten in pingpong by Erdős, then already middleaged; he returned to New Jersey determined to improve his game, and eventually became Bell Labs champion and won a state title in the game.^{ [1]} Graham later popularized the concept of the Erdős number, a measure of distance from Erdős in the collaboration network of mathematicians;^{ [10]}^{ [8]} his many works with Erdős include two books of open problems^{ [B1]}^{ [B5]} and Erdős's final posthumous paper.^{ [A15]} Graham divorced in the 1970s; in 1983 he married his Bell Labs colleague and frequent coauthor Fan Chung.^{ [1]}
While at Bell Labs, Graham also took a position at Rutgers University as University Professor of Mathematical Sciences in 1986, and served a term as president of the American Mathematical Society from 1993 to 1994. He became Chief Scientist of the labs in 1995.^{ [1]} He retired from AT&T in 1999 after 37 years of service there,^{ [11]} and moved to the University of California, San Diego (UCSD), as the Irwin and Joan Jacobs Endowed Professor of Computer and Information Science.^{ [1]}^{ [8]} At UCSD, he also became chief scientist at the California Institute for Telecommunications and Information Technology.^{ [8]}^{ [5]} In 2003–04, he was president of the Mathematical Association of America.^{ [1]}
Graham died of bronchiectasis^{ [12]} on July 6, 2020, aged 84, in La Jolla, California.^{ [6]}^{ [13]}
Contributions
Graham made important contributions in multiple areas of mathematics and theoretical computer science. He published about 400 papers, a quarter of those with Chung,^{ [14]} and six books, including Concrete Mathematics with Donald Knuth and Oren Patashnik.^{ [B4]} The Erdős Number Project lists him as having nearly 200 coauthors.^{ [15]} He was the doctoral advisor of nine students, one each at the City University of New York and Rutgers University while he was at Bell Labs, and seven at UC San Diego.^{ [9]}
Notable topics in mathematics named after Graham include the Erdős–Graham problem on Egyptian fractions, the Graham–Rothschild theorem in the Ramsey theory of parameter words and Graham's number derived from it, the Graham–Pollak theorem and Graham's pebbling conjecture in graph theory, the Coffman–Graham algorithm for approximate scheduling and graph drawing, and the Graham scan algorithm for convex hulls. He also began the study of primefree sequences, the Boolean Pythagorean triples problem, the biggest little polygon, and square packing in a square.
Graham was one of the contributors to the publications of G. W. Peck, a pseudonymous mathematical collaboration named for the initials of its members, with Graham as the "G".^{ [16]}
Number theory
Graham's doctoral dissertation was in number theory, on Egyptian fractions,^{ [7]}^{ [9]} as is the Erdős–Graham problem on whether every partition of the integers into finitely many classes has a class whose reciprocals sum to one. A proof was published by Ernie Croot in 2003.^{ [17]} Another of Graham's papers on Egyptian fractions was published in 2015 with Steve Butler and (nearly 20 years posthumously) Erdős; it was the last of Erdős's papers to be published, making Butler his 512th coauthor.^{ [A15]}^{ [18]}
In a 1964 paper, Graham began the study of primefree sequences by observing that there exist sequences of numbers, defined by the same recurrence relation as the Fibonacci numbers, in which none of the sequence elements is prime.^{ [A64]} The challenge of constructing more such sequences was later taken up by Donald Knuth and others.^{ [19]} Graham's 1980 book with Erdős, Old and new results in combinatorial number theory, provides a collection of open problems from a broad range of subareas within number theory.^{ [B1]}
Ramsey theory
The Graham–Rothschild theorem in Ramsey theory was published by Graham and Bruce Rothschild in 1971, and applies Ramsey theory to combinatorial cubes in combinatorics on words.^{ [A71a]} Graham gave a large number as an upper bound for an instance of this theorem, now known as Graham's number, which was listed in the Guinness Book of Records as the largest number ever used in a mathematical proof,^{ [20]} although it has since then been surpassed by even larger numbers such as TREE(3).^{ [21]}
Graham offered a monetary prize for solving the Boolean Pythagorean triples problem, another problem in Ramsey theory; the prize was claimed in 2016.^{ [22]} Graham also published two books on Ramsey theory.^{ [B2]}^{ [B3]}
Graph theory
The Graham–Pollak theorem, which Graham published with Henry O. Pollak in two papers in 1971 and 1972,^{ [A71b]}^{ [A72a]} states that if the edges of an vertex complete graph are partitioned into complete bipartite subgraphs, then at least subgraphs are needed. Graham and Pollak provided a simple proof using linear algebra; despite the combinatorial nature of the statement and multiple publications of alternative proofs since their work, all known proofs require linear algebra.^{ [23]}
Soon after research in quasirandom graphs began with the work of Andrew Thomason, Graham published in 1989 a result with Chung and R. M. Wilson that has been called the "fundamental theorem of quasirandom graphs", stating that many different definitions of these graphs are equivalent.^{ [A89a]}^{ [24]}
Graham's pebbling conjecture, appearing in a 1989 paper by Chung, concerns the pebbling number of Cartesian products of graphs. As of 2019^{ [update]}, it remains unsolved.^{ [25]}
Packing, scheduling, and approximation algorithms
Graham's early work on job shop scheduling^{ [A66]}^{ [A69]} introduced the worstcase approximation ratio into the study of approximation algorithms, and laid the foundations for the later development of competitive analysis of online algorithms.^{ [26]} This work was later recognized to be important also for the theory of bin packing,^{ [27]} an area that Graham later worked in more explicitly.^{ [A74]}
The Coffman–Graham algorithm, which Graham published with Edward G. Coffman Jr. in 1972,^{ [A72b]} provides an optimal algorithm for twomachine scheduling, and a guaranteed approximation algorithm for larger numbers of machines. It has also been applied in layered graph drawing.^{ [28]}
In a survey article on scheduling articles published in 1979, Graham and his coauthors introduced a threesymbol notation for classifying theoretical scheduling problems according to the system of machines they are to run on, the characteristics of the tasks and resources such as requirements for synchronization or noninterruption, and the performance measure to be optimized.^{ [A79]} This classification has sometimes been called "Graham notation" or "Graham's notation".^{ [29]}
Discrete and computational geometry
Graham scan is a widely used and practical algorithm for convex hulls of twodimensional point sets, based on sorting the points and then inserting them into the hull in sorted order.^{ [30]} Graham published the algorithm in 1972.^{ [A72c]}
The biggest little polygon problem asks for the polygon of largest area for a given diameter. Surprisingly, as Graham observed, the answer is not always a regular polygon.^{ [A75a]} Graham's 1975 conjecture on the shape of these polygons was finally proven in 2007.^{ [31]}
In another 1975 publication, Graham and Erdős observed that for packing unit squares into a larger square with noninteger side lengths, one can use tilted squares to leave an uncovered area that is sublinear in the side length of the larger square, unlike the obvious packing with axisaligned squares.^{ [A75b]} Klaus Roth and Bob Vaughan proved that uncovered area at least proportional to the square root of the side length may sometimes be needed; proving a tight bound on the uncovered area remains an open problem.^{ [32]}
Probability and statistics
In nonparametric statistics, a 1977 paper by Persi Diaconis and Graham studied the statistical properties of Pearson's footrule, a measure of rank correlation that compares two permutations by summing, over each item, the distance between the positions of the item in the two permutations.^{ [A77]} They compared this measure to other rank correlation methods, resulting in the "Diaconis–Graham inequalities"
where is Pearson's footrule, is the number of inversions between the two permutations (a nonnormalized version of the Kendall rank correlation coefficient), and is the minimum number of twoelement swaps needed to obtain one permutation from the other.^{ [33]}
The Chung–Diaconis–Graham random process is a random walk on the integers modulo an odd integer , in which at each step one doubles the previous number and then randomly adds zero, , or (modulo ). In a 1987 paper, Chung, Diaconis, and Graham studied the mixing time of this process, motivated by the study of pseudorandom number generators.^{ [A87]}^{ [34]}
Juggling
Graham became a capable juggler beginning at age 15, and was practiced in juggling up to six balls.^{ [4]} (Although a published photo shows him juggling twelve balls,^{ [5]} it is a manipulated image.^{ [3]}) He taught Steve Mills, a repeat winner of the International Jugglers' Association championships, how to juggle, and his work with Mills helped inspire Mills to develop the Mills' Mess juggling pattern. As well, Graham made significant contributions to the theory of juggling, including a sequence of publications on siteswaps. In 1972 he was elected president of the International Jugglers' Association.^{ [4]}
Awards and honors
In 2003, Graham won the American Mathematical Society's annual Leroy P. Steele Prize for Lifetime Achievement. The prize cited his contributions to discrete mathematics, his popularization of mathematics through his talks and writing, his leadership at Bell Labs, and his service as president of the society.^{ [2]} He was one of five inaugural winners of the George Pólya Prize of the Society for Industrial and Applied Mathematics, sharing it with fellow Ramsey theorists Klaus Leeb, Bruce Rothschild, Alfred Hales, and Robert I. Jewett.^{ [35]} He was also one of two inaugural winners of the Euler Medal of the Institute of Combinatorics and its Applications, the other being Claude Berge.^{ [36]}
Graham was elected to the National Academy of Sciences in 1985.^{ [37]} In 1999 he was inducted as an ACM Fellow "for seminal contributions to the analysis of algorithms, in particular the worstcase analysis of heuristics, the theory of scheduling, and computational geometry".^{ [38]} He became a Fellow of the Society for Industrial and Applied Mathematics in 2009; the fellow award cited his "contributions to discrete mathematics and its applications".^{ [39]} In 2012 he became a fellow of the American Mathematical Society.^{ [40]}
Graham was an invited speaker at the 1982 International Congress of Mathematicians (held 1983 in Warsaw),^{ [13]} speaking on "Recent developments in Ramsey theory".^{ [A84]} He was twice Josiah Willard Gibbs Lecturer, in 2001 and 2015.^{ [13]} The Mathematical Association of America awarded him both the Carl Allendoerfer Prize for his paper "Steiner Trees on a Checkerboard" with Chung and Martin Gardner in Mathematics Magazine (1989),^{ [A89b]}^{ [41]} and the Lester R. Ford Award for his paper "A whirlwind tour of computational geometry" with Frances Yao in the American Mathematical Monthly (1990).^{ [A90]}^{ [42]} His book Magical Mathematics with Persi Diaconis^{ [B6]} won the Euler Book Prize.^{ [43]}
The proceedings of the Integers 2005 conference was published as a festschrift for Ron Graham's 70th birthday.^{ [44]} Another festschrift, stemming from a conference held in 2015 in honor of Graham's 80th birthday, was published in 2018 as the book Connections in discrete mathematics: a celebration of the work of Ron Graham.^{ [45]}
Selected publications
Books
B1.  Old and new results in combinatorial number theory. With
Paul Erdős. Monographie 28, L'Enseignement Mathématique, 1980.^{
[46]}

B2.  Ramsey Theory. With
Bruce Rothschild and
Joel Spencer. Wiley, 1980; 2nd ed., 1990.^{
[47]}

B3.  Rudiments of Ramsey Theory. American Mathematical Society, 1981; 2nd ed., with
Steve Butler, 2015.^{
[48]}

B4. 
Concrete Mathematics: a foundation for computer science. With
Donald Knuth and
Oren Patashnik. AddisonWesley, 1989; 2nd ed., 1994.^{
[49]}

B5. 
Erdős on Graphs. His legacy of unsolved problems. With
Fan Chung. A K Peters, 1998.^{
[50]}

B6.  Magical Mathematics: the mathematical ideas that animate great magic tricks. With
Persi Diaconis. Princeton University Press, 2011.^{
[51]}

Edited volumes
V1.  Handbook of Combinatorics. Edited with
Martin Grötschel and
László Lovász. MIT Press, 1995.^{
[52]}

V2.  The mathematics of Paul Erdős. Edited with
Jaroslav Nešetřil. 2 volumes. Springer, 1997; 2nd ed., 2013.^{
[53]}

Articles
A64. 
Graham, Ronald L. (1964).
"A Fibonaccilike sequence of composite numbers" (PDF).
Mathematics Magazine. 37 (5): 322–324.
doi:
10.2307/2689243.
JSTOR
2689243.
MR
1571455.
Zbl
0125.02103.

A66.  Graham, R. L. (1966).
"Bounds for certain multiprocessing anomalies" (PDF).
Bell System Technical Journal. 45 (9): 1563–1581.
doi:
10.1002/j.15387305.1966.tb01709.x.
Zbl
0168.40703.

A69.  Graham, R. L. (1969).
"Bounds on multiprocessing timing anomalies" (PDF).
SIAM Journal on Applied Mathematics. 17 (2): 416–429.
doi:
10.1137/0117039.
MR
0249214.
Zbl
0188.23101.

A71a.  Graham, R. L.;
Rothschild, B. L. (1971).
"Ramsey's theorem for nparameter sets" (PDF).
Transactions of the American Mathematical Society. 159: 257–292.
doi:
10.1090/S00029947197102843528.
JSTOR
1996010.
MR
0284352.
Zbl
0233.05003.

A71b.  Graham, R. L.;
Pollak, H. O. (1971).
"On the addressing problem for loop switching" (PDF).
Bell System Technical Journal. 50 (8): 2495–2519.
doi:
10.1002/j.15387305.1971.tb02618.x.
MR
0289210.
Zbl
0228.94020.

A72a.  Graham, R. L.;
Pollak, H. O. (1972). "On embedding graphs in squashed cubes".
Graph theory and applications (Proc. Conf., Western Michigan Univ., Kalamazoo, Mich., 1972; dedicated to the memory of J. W. T. Youngs) (PDF). Lecture Notes in Mathematics. Vol. 303. pp. 99–110.
MR
0332576.
Zbl
0251.05123.

A72b. 
Coffman, E. G. Jr.;
Graham, R. L. (1972).
"Optimal scheduling for twoprocessor systems" (PDF).
Acta Informatica. 1 (3): 200–213.
doi:
10.1007/bf00288685.
MR
0334913.
S2CID
40603807.
Zbl
0248.68023.

A72c.  Graham, R. L. (1972).
"An efficient algorithm for determining the convex hull of a finite planar set" (PDF).
Information Processing Letters. 1 (4): 132–133.
doi:
10.1016/00200190(72)900452.
Zbl
0236.68013.

A74. 
Johnson, D. S.; Demers, A.;
Ullman, J. D.;
Garey, M. R.; Graham, R. L. (1974).
"Worstcase performance bounds for simple onedimensional packing algorithms" (PDF).
SIAM Journal on Computing. 3 (4): 299–325.
doi:
10.1137/0203025.
MR
0434396.
Zbl
0297.68028.

A75a. 
Graham, R. L. (1975).
"The largest small hexagon" (PDF).
Journal of Combinatorial Theory. Series A. 18 (2): 165–170.
doi:
10.1016/00973165(75)900047.
MR
0360353.
Zbl
0299.52006.

A75b. 
Erdős, P.; Graham, R. L. (1975).
"On packing squares with equal squares" (PDF).
Journal of Combinatorial Theory. Series A. 19: 119–123.
doi:
10.1016/00973165(75)900990.
MR
0370368.
Zbl
0324.05018.

A77. 
Diaconis, Persi; Graham, R. L. (1977). "Spearman's footrule as a measure of disarray".
Journal of the Royal Statistical Society. 39 (2): 262–268.
doi:
10.1111/j.25176161.1977.tb01624.x.
JSTOR
2984804.
MR
0652736.
Zbl
0375.62045.

A79.  Graham, R. L.;
Lawler, E. L.;
Lenstra, J. K.;
Rinnooy Kan, A. H. G. (1979).
"Optimization and approximation in deterministic sequencing and scheduling: a survey" (PDF). Annals of Discrete Mathematics. 5: 287–326.
doi:
10.1016/S01675060(08)70356X.
ISBN
9780080867670.
MR
0558574.
Zbl
0411.90044.

A84.  Graham, R. L. (1984).
"Recent developments in Ramsey theory" (PDF). Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983). Warsaw: PWN. pp. 1555–1567.
MR
0804796.
Zbl
0572.05009.

A87. 
Chung, F. R. K.;
Diaconis, Persi; Graham, R. L. (1987).
"Random walks arising in random number generation" (PDF).
Annals of Probability. 15 (3): 1148–1165.
doi:
10.1214/aop/1176992088.
JSTOR
2244046.
MR
0893921.
Zbl
0622.60016.

A89a. 
Chung, F. R. K.; Graham, R. L.;
Wilson, R. M. (1989).
"Quasirandom graphs" (PDF).
Combinatorica. 9 (4): 345–362.
doi:
10.1007/BF02125347.
MR
1054011.
S2CID
17166765.
Zbl
0715.05057.

A89b. 
Chung, Fan;
Gardner, Martin; Graham, Ron (1989).
"Steiner trees on a checkerboard" (PDF).
Mathematics Magazine. 62 (2): 83–96.
doi:
10.2307/2690388.
JSTOR
2690388.
MR
0991536.
Zbl
0681.05018.

A90.  Graham, Ron;
Yao, Frances (1990).
"A whirlwind tour of computational geometry" (PDF).
American Mathematical Monthly. 97 (8): 687–701.
doi:
10.2307/2324575.
JSTOR
2324575.
MR
1072812.
Zbl
0712.68097.

A15. 
Butler, Steve;
Erdős, Paul; Graham, Ron (2015).
"Egyptian fractions with each denominator having three distinct prime divisors" (PDF). Integers. 15: A51.
MR
3437526.
Zbl
1393.11030.

References
 ^ ^{a} ^{b} ^{c} ^{d} ^{e} ^{f} ^{g} ^{h} ^{i} ^{j} ^{k} ^{l} O'Connor, John J.; Robertson, Edmund F. "Ronald Graham". MacTutor History of Mathematics archive. University of St Andrews.
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 ^ ^{a} ^{b} ^{c} Horgan, John (March 1997). "Profile: Ronald L. Graham – Juggling Act". Scientific American. 276 (3): 28–30. doi: 10.1038/scientificamerican039728.
 ^ ^{a} ^{b} ^{c} "Ron Graham Obituary". International Jugglers' Association. July 9, 2020. Retrieved July 13, 2020.
 ^ ^{a} ^{b} ^{c} "Juggling Numbers: UC San Diego Professor Honored for Work in Applied Mathematics and Computational Science". California Institute for Telecommunications and Information Technology. May 4, 2009. Retrieved July 9, 2020.
 ^ ^{a} ^{b} "Ronald Lewis Graham, 2003–2004 MAA President". Mathematical Association of America. July 7, 2020. Retrieved July 7, 2020.
 ^ ^{a} ^{b} ^{c} ^{d} Albers, Donald J. (November 1996). "A Nice Genius". Math Horizons. 4 (2): 18–23. doi: 10.1080/10724117.1996.11974993. JSTOR 25678089.
 ^ ^{a} ^{b} ^{c} ^{d} ^{e} Bigelow, Bruce V. (March 18, 2003). "You can count on him: Math expert coolly juggles scientific puzzles and six or seven balls" (PDF). The San Diego UnionTribune.
 ^ ^{a} ^{b} ^{c} Ronald Graham at the Mathematics Genealogy Project
 ^ Hoffman, Paul (1998). The man who loved only numbers: the story of Paul Erdős and the search for mathematical truth. Hyperion. pp. 109–110. ISBN 9780786863624.
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 ^ Ron Graham obituary by Colm Mulcahy, The Guardian, August 3, 2020
 ^ "Erdos1: coauthors of Paul Erdős, together with their coauthors listed beneath them". Erdős Number Project. Retrieved July 12, 2020.
 ^ Peck, G. W. (2002). "Kleitman and combinatorics: a celebration". Discrete Mathematics. 257 (2–3): 193–224. doi: 10.1016/S0012365X(02)005952. MR 1935723. See in particular Section 4, "The mysterious G. W. Peck", pp. 216–219.

^ Croot, Ernest S., III (2003). "On a coloring conjecture about unit fractions".
Annals of Mathematics. 157 (2): 545–556.
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Bibcode:
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10.4007/annals.2003.157.545.
MR
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S2CID
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{{ cite journal}}
: CS1 maint: multiple names: authors list ( link)  ^ Roberts, Siobhan (December 10, 2015). "New Erdős Paper Solves Egyptian Fraction Problem". Simons Foundation.
 ^ Knuth, Donald E. (1990). "A Fibonaccilike sequence of composite numbers". Mathematics Magazine. 63 (1): 21–25. doi: 10.2307/2691504. JSTOR 2691504. MR 1042933.
 ^ Guinness Book of World Records (Rev. American ed.). Sterling Publishing. 1980. p. 193. ISBN 0806901683.
 ^ Bennett, Jay (October 20, 2017). "The Enormity of the Number TREE(3) Is Beyond Comprehension". Popular Mechanics. Retrieved July 9, 2020.
 ^ Lamb, Evelyn (May 26, 2016). "Twohundredterabyte maths proof is largest ever". Nature. 534 (7605): 17–18. Bibcode: 2016Natur.534...17L. doi: 10.1038/nature.2016.19990. PMID 27251254.
 ^ Aigner, Martin; Ziegler, Günter M. (2018). Proofs from THE BOOK (6th ed.). Springer. pp. 79–80. doi: 10.1007/9783662572658_15. ISBN 9783662572658.
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 ^ Pleanmani, Nopparat (2019). "Graham's pebbling conjecture holds for the product of a graph and a sufficiently large complete bipartite graph". Discrete Mathematics, Algorithms and Applications. 11 (6): 1950068, 7. doi: 10.1142/s179383091950068x. MR 4044549. S2CID 204207428.
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 ^ Bastert, Oliver; Matuszewski, Christian (2001). "Layered drawings of digraphs". In Kaufmann, Michael; Wagner, Dorothea (eds.). Drawing Graphs: Methods and Models. Lecture Notes in Computer Science. Vol. 2025. SpringerVerlag. pp. 87–120. doi: 10.1007/3540449698_5.
 ^ For a recent example, see e.g. Cygan, Marek; Pilipczuk, Marcin; Pilipczuk, Michał; Wojtaszczyk, Jakub Onufry (2014). "Scheduling partially ordered jobs faster than ". Algorithmica. 68 (3): 692–714. doi: 10.1007/s0045301296947. MR 3160651.
 ^ De Berg, Mark; Cheong, Otfried; Van Kreveld, Marc; Overmars, Mark (2008). Computational Geometry: Algorithms and Applications. Berlin: Springer. pp. 2–14. doi: 10.1007/9783540779742. ISBN 9783540779735.
 ^ Foster, Jim; Szabo, Tamas (2007). "Diameter graphs of polygons and the proof of a conjecture of Graham". Journal of Combinatorial Theory. Series A. 114 (8): 1515–1525. doi: 10.1016/j.jcta.2007.02.006. MR 2360684..
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 ^ Hadjicostas, Petros; Monico, Chris (2015). "A new inequality related to the DiaconisGraham inequalities and a new characterisation of the dihedral group". The Australasian Journal of Combinatorics. 63: 226–245. MR 3403376.
 ^ Hildebrand, Martin (2019). "On a lower bound for the ChungDiaconisGraham random process". Statistics & Probability Letters. 152: 121–125. doi: 10.1016/j.spl.2019.04.020. MR 3953053. S2CID 164932860.
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^ Butler, Steve; Cooper, Joshua; Hurlbert, Glenn, eds. (2018). Connections in discrete mathematics: a celebration of the work of Ron Graham. Cambridge University Press.
ISBN
9781316607886. Reviews: Hopkins, David (June 2019). The Mathematical Gazette. 103 (557): 374–375.
doi:
10.1017/mag.2019.82.
S2CID
241732634.
{{ cite journal}}
: CS1 maint: untitled periodical ( link) Kleitman, Daniel (December 2019). "Only connect". Inferences. 5 (1). 
^ Review of Old and new problems and results in combinatorial number theory:
 Eggan, L. C. (1982).
Mathematical Reviews.
MR
0592420.
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 Eggan, L. C. (1982).
Mathematical Reviews.
MR
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^ Reviews of Ramsey Theory:
 Li, KoWei.
zbMATH.
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: CS1 maint: untitled periodical ( link) Updated for 2nd ed., Zbl 0705.05061.  Hindman, Neil (September–October 1981).
American Scientist. 69 (5): 572.
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27850688.
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: CS1 maint: untitled periodical ( link)  Graver, J. E. (1982).
Mathematical Reviews.
MR
0591457.
{{ cite journal}}
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Faudree, Ralph (January 1982).
Bulletin of the American Mathematical Society. 6 (1): 113–117.
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10.1090/s027309791982149825.
{{ cite journal}}
: CS1 maint: untitled periodical ( link)  Vestal, Donald L. (December 2006). "Review". MAA Reviews. Mathematical Association of America.
 Li, KoWei.
zbMATH.
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^ Reviews of Rudiments of Ramsey Theory:
 Hindman, N. (1982).
Mathematical Reviews.
MR
0608630.
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Trotter, W.
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Vaseršteĭn, L. N. (September 1982).
Bulletin of the London Mathematical Society. 14 (5): 458–460.
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{{ cite journal}}
: CS1 maint: untitled periodical ( link)  Lacey, H. E. (September–October 1982).
American Scientist. 70 (5): 546–547.
JSTOR
27851705.
{{ cite journal}}
: CS1 maint: untitled periodical ( link)  Stenger, Allen (June 2016). "Review". MAA Reviews. Mathematical Association of America.
 Grossman, Jerrold W.
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MR
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Mathematical Reviews.
MR
0608630.

^ Reviews of Concrete Mathematics:

Bressoud, David M.
zbMATH.
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0668.00003.
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: CS1 maint: untitled periodical ( link) Review of 2nd ed, Zbl 0836.00001.  Liu, Stanley (September–October 1989). "From the discrete to the continuous". Computers in Physics. 3 (5): 106. doi: 10.1063/1.4822863.
 van Lint, J. H. (1990). "Review". Zentralblatt für Didaktik der Mathematik. 90 (1): 4–5.
 Strehl, Volker (1991).
Mathematical Reviews.
MR
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: CS1 maint: untitled periodical ( link) Review of 2nd ed (1997), MR 1397498.  Pokhodzei, B. B. (1991). "Review". Diskretnaya Matematika (in Russian). 3 (1): 155–156.
 Jelliss, G. P. (March 1991).
The Mathematical Gazette. 75 (471): 117.
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10.2307/3619021.
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{{ cite journal}}
: CS1 maint: untitled periodical ( link)  Bender, Edward A. (October 1991).
American Mathematical Monthly. 98 (8): 779–780.
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10.2307/2324448.
JSTOR
2324448.
MR
1541984.
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: CS1 maint: untitled periodical ( link)  Stenger, Allan (November 2010). "Review". MAA Reviews. Mathematical Association of America.

Bressoud, David M.
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^ Reviews of Erdős on Graphs:

Faudree, R.
zbMATH.
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0890.05049.
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Schelp, R. H. (1999).
Mathematical Reviews.
MR
1601954.
{{ cite journal}}
: CS1 maint: untitled periodical ( link)  Beezer, Robert A. (March 2000).
SIAM Review. 42 (1): 143–145.
JSTOR
2653387.
{{ cite journal}}
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Tutte, W. T. (September 2000).
SIAM Review. 42 (3): 548–549.
JSTOR
2653326.
{{ cite journal}}
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Hobbs, Arthur M. (April 2001).
American Mathematical Monthly. 108 (4): 379–381.
doi:
10.2307/2695262.
JSTOR
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{{ cite journal}}
: CS1 maint: untitled periodical ( link)  Crilly, Tony (July 2001).
The Mathematical Gazette. 85 (503): 375–377.
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10.2307/3622075.
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S2CID
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Faudree, R.
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^ Reviews of Magical Mathematics:
 Rogovchenko, Yuri V.
zbMATH.
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{{ cite journal}}
: CS1 maint: untitled periodical ( link)  Young, Jeffrey R. (October 16, 2011). "The magical mind of Persi Diaconis". The Chronicle of Higher Education.
 Cook, John D. (November 2011). "Review". MAA Reviews. Mathematical Association of America.
 Howls, C. J. (November 23, 2011). "To create illusions, Fibonacci and algorithms are as important as sleight of hand". Times Higher Education.
 Stone, Alex (December 10, 2011). "Pick a card, any card". The Wall Street Journal.
 Benjamin, Arthur (2012). "Featured review" (PDF). SIAM Review. 54 (3): 609–612. doi: 10.1137/120973238. JSTOR 41642632. MR 2985718.
 Wiseman, Richard (February 2012). "Just like that". Nature Physics. 8 (2): 104–105. Bibcode: 2012NatPh...8..104W. doi: 10.1038/nphys2225.
 Davis, Philip J. (March 18, 2012). "Tricky mathematics". SIAM News.
 Ó Cairbre, Fiacre (Summer 2012). "Review" (PDF). Irish Mathematical Society Bulletin. 69: 60–62.
 Castrillón López, Marco (July 2012). "Review". EMS Reviews. European Mathematical Society.
 Van Osdol, Donovan H. (August 2012).
Notices of the American Mathematical Society. 59 (7): 960–961.
doi:
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: CS1 maint: untitled periodical ( link)  Bledsoe, Christie (April 2013). The Mathematics Teacher. 106 (8): 637.
doi:
10.5951/mathteacher.106.8.0637.
JSTOR
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{{ cite journal}}
: CS1 maint: untitled periodical ( link)  Robert, Christian (April 2013). Chance. 26 (2): 50–51.
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: CS1 maint: untitled periodical ( link)  Scarrabelotti, Jack (2014). "Review". Australian Mathematics Teacher. 70 (1): 29.
 Brown, Jill (2015). "Review". Australian Senior Mathematics Journal. 29 (2): 62.
 Rogovchenko, Yuri V.
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^ Reviews of Handbook of Combinatorics:

Wilf, Herbert S. (March 1997).
The Mathematical Intelligencer. 19 (2): 68–69.
doi:
10.1007/bf03024438.
{{ cite journal}}
: CS1 maint: untitled periodical ( link)  Gasarch, William (June 1999). "Review" (PDF). ACM SIGACT News. 30 (2): 7. doi: 10.1145/568547.568551. S2CID 3200815.

Wilf, Herbert S. (March 1997).
The Mathematical Intelligencer. 19 (2): 68–69.
doi:
10.1007/bf03024438.

^ Reviews of The Mathematics of Paul Erdős:

Soifer, A.
zbMATH.
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{{ cite journal}}
: CS1 maint: untitled periodical ( link)  Bauer, Craig P. (December 2013). "Review". MAA Reviews. Mathematical Association of America.

Soifer, A.
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External links
 Graham's UCSD Faculty Research Profile
 Papers of Ron Graham – a comprehensive archive of the papers written by Ron Graham
 About Ron Graham – a page summarizing some aspects of Graham's life and mathematics – part of Fan Chung's website
 "Simons Foundation: Ronald Graham (1935–2020)". Simons Foundation. January 11, 2016. – Extended video interview.
 "Three Mathematicians We Lost in 2020: John Conway, Ronald Graham, and Freeman Dyson all explored the world with their minds" Rockmore, Dan. (December 31, 2020) The New Yorker.
 Buhler, Joe; Butler, Steve; Spencer, Joel (December 2021). "Ronald Lewis Graham (1935–2020)" (PDF). Notices of the American Mathematical Society. 68 (11): 1931–1950. doi: 10.1090/noti2382.
 Ronald Graham publications indexed by Google Scholar
 1935 births
 2020 deaths
 20thcentury American mathematicians
 21stcentury American mathematicians
 Fellows of the American Mathematical Society
 Fellows of the Association for Computing Machinery
 Fellows of the Society for Industrial and Applied Mathematics
 Graph theorists
 Mathematicians from California
 Mathematics popularizers
 Members of the United States National Academy of Sciences
 People from Taft, California
 Presidents of the American Mathematical Society
 Presidents of the Mathematical Association of America
 Researchers in geometric algorithms
 Scientists at Bell Labs
 University of Alaska Fairbanks alumni
 University of California, Berkeley alumni
 Rutgers University faculty
 University of California, San Diego faculty
 Deaths from lung disease