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Prize: Delbert Ray Fulkerson Prize (AMS-MOS)

Delbert Ray Fulkerson Prize (AMS-MOS) 2018 Thomas Rothvoß; Peter Allen ; Julia Böttcher; Simon Griffiths; Yoshiharu Kohayakawa; Robert Morris

Fourteenth award: to Peter Allen, Julia Böttcher, Simon Griffiths, Yoshiharu Kohayakawa, Robert Morris for "The chromatic thresholds of graphs", *Adv. Math.* 235, 261-295 (2013). Also awarded to Thomas Rothvoß for " The Matching Polytope has Exponential Extension Complexity.", *J. ACM *64(6): 41:1-41:19 (2017).

Delbert Ray Fulkerson Prize (AMS-MOS) 2015 Francisco Santos

Thirteenth award: to Francisco Santos for "A Counterexample to the Hirsch Conjecture", Annals of Mathematics, 2012.

Delbert Ray Fulkerson Prize (AMS-MOS) 2012 Sanjeev Arora; Satish Rao; Umesh Vazirani; Anders Johansson; Jeff Kahn; Van H. Vu; László Lovász; Balázs Szegedy

Twelth award: to Sanjeev Arora, Satish Rao, and Umesh Vazirani for improving the approximation ratio for graph separators and related problems. ToAnders Johansson, Jeff Kahn, and Van H. Vu for determining the threshold of edge density above which a random graph can be covered by disjoint copies of a given smaller graph. To László Lovász and Balázs Szegedy for characterizing subgraph multiplicity in sequences of dense graphs.

Delbert Ray Fulkerson Prize (AMS-MOS) 2009 Maria Chudnovsky; Neil Robertson; Paul Seymour; Robin Thomas; Daniel A. Spielman; Shang-Hua Teng; Thomas C. Hales; Samuel P. Ferguson

Eleventh award: to M. Chudnovsky, N. Robertson, P. Seymour, and R. Thomas, "The strong perfect graph theorem," *Annals of Mathematics*, 164 (2006) 51-229; and to D. A. Spielman and S.-H. Teng, "Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time", *Journal of ACM* 51 (2004) 385-463; and to Thomas C. Hales, "A proof of the Kepler conjecture", *Annals of Mathematics* 162 (2005) 1063-1183; and to Samuel P. Ferguson, "Sphere Packings, V. Pentahedral Prisms", *Discrete and Computational Geometry* 33 (2006) 167-204.

Prize announcement as seen in *Notices of the AMS*.

Delbert Ray Fulkerson Prize (AMS-MOS) 2006 Manindra Agrawal; Neeraj Kayal; Nitin Saxena; Mark Jerrum; Alistair Sinclair; Eric Vigoda; Neil Robertson; Paul D. Seymour

Tenth award: to Manindra Agrawal, Neeraj Kayal and Nitin Saxena, "PRIMES is in P," *Annals of Mathematics*, Volume 160, issue 2, 2004, Pages 781--793; and to Mark Jerrum, Alistair Sinclair and Eric Vigoda, "A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries," *J. ACM*, Volume 51, Issue 4, 2004, Pages 671--697; and to Neil Robertson and Paul D. Seymour, "Graph Minors. XX. Wagner's conjecture," *Journal of Combinatorial Theory*, Series B, Volume 92, Issue 2 , 2004, Pages 325--357.

Prize announcement as seen in *Notices of the AMS*.

Delbert Ray Fulkerson Prize (AMS-MOS) 2003 J. F. Geelen; A. M. H. Gerards; A. Kapoor; Bertrand Guenin; Satoru Iwata; Lisa Fleischer; Satoru Fujishige; Alexander Schrijver

Ninth award: to J. F. Geelen, A. M. H. Gerards and A. Kapoor, for "The Excluded Minors for GF(4)-Representable Matroids," Journal of Combinatorial Theory Series B, 79 (2000), no. 2, 247--299; and to Bertrand Guenin for "A characterization of weakly bipartite graphs," *Journal of Combinatorial Theory Series B*, 83 (2001), no. 1, 112--168; and to Satoru Iwata, Lisa Fleischer, and Satoru Fujishige for "A combinatorial strongly polynomial algorithm for minimizing submodular functions," Journal of the ACM, 48, July 2001, no. 4, 761--777; and to Alexander Schrijver for "A combinatorial algorithm minimizing submodular functions in strongly polynomial time," *Journal of Combinatorial Theory Series B*, 80 (2000), no. 2, 346--355.

Prize announcement as seen in *Notices of the AMS*.

Delbert Ray Fulkerson Prize (AMS-MOS) 2000 Michel X. Goemans; David P. Williamson; Michele Conforti; Gerard Cornuejols; M. R. Rao

Eighth award: to Michel X. Goemans and David P. Williamson for "Improved approximation algorithms for the maximum cut and satisfiability probelsm using semi-definite programming", *Journal of the Association for Computing Machinery*, 42 (1995), no. 6, pages 1115-1145; and to Michele Conforti, Gerard Cornuejols, and M. R. Rao for "Decomposition of balanced matrices", *Journal of Combinatorial Theory*, Series B, 77 (1999), no. 2, pages 292-406.

Prize announcement as seen in *Notices of the AMS*.

Delbert Ray Fulkerson Prize (AMS-MOS) 1997 Jeong Han Kim

Seventh award: to Jeong Han Kim for "The Ramsey Number R(3,t) Has Order of Magnitude t^{2}/log t," which appeared in *Random Structures and Algorithms*, volume 7, issue 3, 1995, pages 173-207.

Prize announcement as seen in *Notices of the AMS*.

Delbert Ray Fulkerson Prize (AMS-MOS) 1994 Louis Billera; Gil Kalai; Neil Robertson; Paul D. Seymour; Robin Thomas

Sixth award: to Louis Billera for "Homology of smooth splines: Generic triangulations and a conjecture of Strang", *Transactions of the AMS*, volume 310 (1988) pp. 325-340; to Gil Kalai for Upper bounds for the diameter and height of graphs of the convex polyhedra, Discrete and Computational Geometry, volume 8 (1992) pp. 363-372; and to Neil Robertson, Paul D. Seymour, and Robin Thomas for Hadwiger's conjecture for K6; free graphs, Combinatorica, volume 13 (1993) pp. 279-361.

Delbert Ray Fulkerson Prize (AMS-MOS) 1991 Martin Dyer; Alan Frieze; Ravi Kannan; Alfred Lehman; W. Cook; P. D. Seymour; Nikolai E. Mnev

Fifth award: to Martin Dyer, Alan Frieze, and Ravi Kannan for *A random polynomial time algorithm for approximating the volume of convex bodies*, Journal of the Association for Computing Machinery, volume 38/1 (1991) pp. 1-17; to Alfred Lehman for *The width-length inequality and degenerate projective planes*, W. Cook and P. D. Seymour (eds.), Polyhedral Combinatorics, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, volume 1, (American Mathematical Society, 1990) pp. 101-105; and to Nikolai E. Mnev for *The universality theorems on the classification problem of configuration varieties and convex polytope varieties*, O. Ya. Viro (ed.), Topology and Geometry-Rohlin Seminar, Lecture Notes in Mathematics 1346 (Springer-Verlag, Berlin, 1988) pp. 527-544.

Delbert Ray Fulkerson Prize (AMS-MOS) 1988 Eva Tardos; Narendra Karmarkar

Fourth award: to Eva Tardos for *A strongly polynomial minimum cost circulation algorithm*, Combinatorica, volume 5 (1985), pp. 247-256; and to Narendra Karmarkar for A new polynomial-time algorithm for linear programming, Combinatorica, volume 4 (1984), pp. 373-395.

Delbert Ray Fulkerson Prize (AMS-MOS) 1985 Jozsef Beck; H. W. Lenstra Jr.; Eugene M. Luks

Third award: to Jozsef Beck, for *Roth's estimate of the discrepancy of integer sequences is nearly sharp*, Combinatorica 1 (4),319-325, (1981); and H. W. Lenstra, Jr., for *Integer programming with a fixed number of variables*, Mathematics of Operations Research 8 (4), 538-548, (1983); and Eugene M. Luks for *Isomorphism of graphs of bounded valence can be tested in polynomial time*, Journal of Computer and System Sciences 25 (1), 42-65, (1982).

Delbert Ray Fulkerson Prize (AMS-MOS) 1982 D.B. Judin; A.S. Nemirovskii; L.G. Khachiyan; G.P. Egorychev; D.I. Falikman; M. Grötschel; L. Lovasz; A. Schrijver

Second award: to D.B. Judin and A.S. Nemirovskii, for *Informational complexity and effective methods of solution for convex extremal problems*, Ekonomika i Matematicheskie Metody 12 (1976), 357-369, and to L. G. Khachiyan for *A polynomial algorithm in linear programming*, Akademiia Nauk SSSR. Doklady 244 (1979), 1093-1096; to G. P. Egorychev, for *The solution of van der Waerden's problem for permanents*, Akademiia Nauk SSSR. Doklady 258 (1981), 1041-1044, and D.I. Falikman, for *A proof of the van der Waerden conjecture on the permanent of a doubly stochastic matrix*, Matematicheskie Zametki 29 (1981), 931-938; and to M. Grötschel, L. Lovasz and A. Schrijver, for *The ellipsoid method and its consequences in combinatorial optimization*, Combinatorica 1 (1981), 169-197.

Delbert Ray Fulkerson Prize (AMS-MOS) 1979 Richard M. Karp; Kenneth Appel; Wolfgang Haken; Paul D. Seymour

First award: to Richard M. Karp, for *On the computational complexity of combinatorial problems*, Networks, volume 5 (1975), pp. 45-68; to Kenneth Appel and Wolfgang Haken, for *Every planar map is four colorable*, Part I: Discharging, Illinois Journal of Mathematics, volume 21 (1977), pp. 429-490; and to Paul D. Seymour, for *The matroids with the max-flow min-cut property*, Journal of Combinatorial Theory, Series B, volume 23 (1977), pp. 189-222.