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1997 Fulkerson Prize

The D. Ray Fulk- paper by Erdo˝s on the symmetric Ramsey number erson Prize in Dis- R(t,t) is generally viewed as the start of the proba- crete Mathematics bilistic method in combinatorics. Since then devel- was awarded on opments in bounds on the Ramsey number have August 25, 1997, been intertwined with developments of the proba- at the opening session of the bilistic method. XVIth Interna- After the symmetric case, the Ramsey number tional Symposium R(3,t) is the most studied. Erdo˝s and Szekeres on Mathematical proved that R(3,t) is O(t2). This upper bound was Programming in improved by Graver and Yackel in 1968 to Lausanne, 2 log log t O(t log t ), and then in 1990 by Ajtai, Komlós, Switzerland. The t2 Photograph by Michael Moore. © 1998 Microsoft Corp. and Szemerédi to O( log t ). The best-known lower prize of $1,500 is 2 Jeong Han Kim bound for R(3,t) was ( t ), proved in a 1961 jointly sponsored log2 t by the AMS and paper by Erdo˝s. the Mathematical Programming Society. Jeong Han Kim’s paperΩ solves this sixty-year-old The prize committee for the 1997 prize con- problem by improving the Erdo˝s lower bound to sisted of Ronald Graham, AT&T Research; Ravi match the upper bound of Ajtai, Komlós, and Sze- Kannan, Yale University; and Éva Tardos (chair), merédi. The paper is a veritable cornucopia of mod- Cornell University. To be eligible, papers had to be published in a recognized journal during the six ern techniques in the probabilistic method; it uses calendar years preceding the year of the Sympo- martingales in a sophisticated way to obtain strong sium. The term “discrete mathematics” is intended large deviation bounds. to include graph theory, networks, mathematical Kim received his Ph.D. in 1993 from Rutgers Uni- programming, applied combinatorics, and related versity, where his advisor was Jeff Kahn. He worked subjects. While research in these areas is usually at AT&T Research for four years before joining the not far removed from practical applications, the Theory Group at Microsoft Research in 1997. judging of papers is based on their mathematical quality and significance. Past recipients of the Fulkerson Prize are: Richard The 1997 Fulkerson prize was awarded to JEONG M. Karp, Kenneth Appel, Wolfgang Haken, and Paul HAN KIM of Microsoft Research for the paper “The D. Seymour (1979); D. B. Judin, A. S. Nemirovskii, L. Ramsey Number R(3,t) Has Order of G. Khachiyan, G. P. Egorychev, D. I. Falikman, M. t2 Magnitude log t”, which appeared in Random Struc- Grötschel, L. Lovasz, and A. Schrijver (1982); Jozsef tures and Algorithms, volume 7, issue 3, 1995, Beck, H. W. Lenstra Jr., and Eugene M. Luks (1985); pages 173–207. Éva Tardos and Narendra Karmarkar (1988); Martin The Ramsey number R(s,t) is the minimum n Dyer, Alan Frieze, Ravi Kannan, Alfred Lehman, and such that every red-blue coloring of the edges of Nikolai E. Mnev (1991); and Lou Billera, Gil Kalai, Neil the complete graph Kn includes either a red com- plete graph on s nodes or a blue complete graph Robertson, Paul D. Seymour, and Robin Thomas on t nodes. The Ramsey number was introduced (1994). by Erdo˝s and Szekeres in a paper in 1935. The 1947 —Éva Tardos, for the prize committee

984 NOTICES OF THE AMS VOLUME 45, NUMBER 8