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The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical Society (AMS). Up to three awards of $1500 each are presented at each (triennial) International Symposium of the MPS. Originally, the prizes were paid out of a memorial fund administered by the AMS that was established by friends of the late Delbert Ray Fulkerson to encourage mathematical excellence in the fields of research exemplified by his work. The prizes are now funded by an endowment administered by MPS. ==Winners== * 1979: * * Richard M. Karp for classifying many important NP-complete problems.〔Richard M. Karp, "On the computational complexity of combinatorial problems", ''Networks'' 5: 45–68, 1975.〕 * * Kenneth Appel and Wolfgang Haken for the four color theorem.〔Kenneth Appel and Wolfgang Haken, "Every planar map is four colorable, Part I: Discharging," ''Illinois Journal of Mathematics'' 21: 429–490, 1977.〕 * * Paul Seymour for generalizing the max-flow min-cut theorem to matroids.〔Paul Seymour , "The matroids with the max-flow min-cut property," ''Journal of Combinatorial Theory'', Series B, 23: 189–222, 1977.〕 * 1982: * * D.B. Judin, Arkadi Nemirovski, Leonid Khachiyan, Martin Grötschel, László Lovász and Alexander Schrijver for the ellipsoid method in linear programming and combinatorial optimization.〔D.B. Judin and Arkadi Nemirovski, "Informational complexity and effective methods of solution for convex extremal problems," ''Ekonomika i Matematicheskie Metody'' 12: 357–369, 1976.〕〔Leonid Khachiyan, "A polynomial algorithm in linear programming," ''Akademiia Nauk SSSR. Doklady'' 244: 1093–1096, 1979.〕〔.〕〔Martin Grötschel, László Lovász and Alexander Schrijver, "The ellipsoid method and its consequences in combinatorial optimization," ''Combinatorica'' 1: 169–197, 1981.〕 * *G. P. Egorychev and D. I. Falikman for proving van der Waerden's conjecture that the matrix with all entries equal has the smallest permanent of any doubly stochastic matrix.〔G. P. Egorychev, "The solution of van der Waerden's problem for permanents," ''Akademiia Nauk SSSR. Doklady'' 258: 1041–1044, 1981.〕〔D. I. Falikman, "A proof of the van der Waerden conjecture on the permanent of a doubly stochastic matrix," ''Matematicheskie Zametki'' 29: 931–938, 1981.〕 * * * 1985: * * Jozsef Beck for tight bounds on the discrepancy of arithmetic progressions.〔Jozsef Beck, "Roth's estimate of the discrepancy of integer sequences is nearly sharp," ''Combinatorica'' 1 (4): 319–325, 1981.〕 * * H. W. Lenstra, Jr. for using the geometry of numbers to solve integer programs with few variables in time polynomial in the number of constraints.〔H. W. Lenstra, Jr., "Integer programming with a fixed number of variables," ''Mathematics of Operations Research'' 8 (4): 538–548, 1983.〕 * * Eugene M. Luks for a polynomial time graph isomorphism algorithm for graphs of bounded maximum degree.〔Eugene M. Luks, "Isomorphism of graphs of bounded valence can be tested in polynomial time," ''Journal of Computer and System Sciences'' 25 (1): 42–65, 1982.〕〔.〕 * 1988: * * Éva Tardos for finding minimum cost circulations in strongly polynomial time.〔Éva Tardos, "A strongly polynomial minimum cost circulation algorithm," ''Combinatorica'' 5: 247-256, 1985.〕 * * Narendra Karmarkar for Karmarkar's algorithm for linear programming.〔Narendra Karmarkar, "A new polynomial-time algorithm for linear programming," ''Combinatorica'' 4:373–395, 1984.〕 * 1991: * * Martin E. Dyer, Alan M. Frieze and Ravindran Kannan for random-walk-based approximation algorithms for the volume of convex bodies.〔Martin E. Dyer, Alan M. Frieze and Ravindran Kannan, "A random polynomial time algorithm for approximating the volume of convex bodies", ''Journal of the ACM'' 38 (1): 1–17, 1991.〕 * * Alfred Lehman for 0,1-matrix analogues of the theory of perfect graphs.〔Alfred Lehman, "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.〕 * * Nikolai E. Mnev for Mnev's universality theorem, that every semialgebraic set is equivalent to the space of realizations of an oriented matroid.〔Nikolai E. Mnev, "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.〕 * 1994: * * Louis Billera for finding bases of piecewise-polynomial function spaces over triangulations of space.〔Louis Billera, "Homology of smooth splines: Generic triangulations and a conjecture of Strang", ''Transactions of the AMS'' 310: 325–340, 1988.〕 * * Gil Kalai for making progress on the Hirsch conjecture by proving subexponential bounds on the diameter of ''d''-dimensional polytopes with ''n'' facets.〔Gil Kalai, "Upper bounds for the diameter and height of graphs of the convex polyhedra", ''Discrete and Computational Geometry'' 8: 363–372, 1992.〕 * * Neil Robertson, Paul Seymour and Robin Thomas for the six-color case of Hadwiger's conjecture.〔Neil Robertson, Paul Seymour and Robin Thomas, "Hadwiger's conjecture for K_6-free graphs," ''Combinatorica'' 13: 279–361, 1993.〕 * 1997: * *Jeong Han Kim for finding the asymptotic growth rate of the Ramsey numbers ''R''(3,''t'').〔.〕 * 2000: * * Michel X. Goemans and David P. Williamson for approximation algorithms based on semidefinite programming.〔Michel X. Goemans and David P. Williamson, "Improved approximation algorithms for the maximum cut and satisfiability probelsm using semi-definite programming", ''Journal of the ACM'' 42 (6): 1115–1145, 1995.〕 * * Michele Conforti, Gérard Cornuéjols, and M. R. Rao for recognizing balanced 0-1 matrices in polynomial time.〔Michele Conforti, Gérard Cornuéjols, and M. R. Rao, "Decomposition of balanced matrices", ''Journal of Combinatorial Theory'', Series B, 77 (2): 292–406, 1999.〕〔.〕 * 2003: * * J. F. Geelen, A. M. H. Gerards and A. Kapoor for the GF(4) case of Rota's conjecture on matroid minors.〔J. F. Geelen, A. M. H. Gerards and A. Kapoor, "The Excluded Minors for GF(4)-Representable Matroids," ''Journal of Combinatorial Theory'', Series B, 79 (2): 247–2999, 2000.〕〔(2003 Fulkerson Prize citation ), retrieved 2012-08-18.〕 * * Bertrand Guenin for a forbidden minor characterization of the weakly bipartite graphs (graphs whose bipartite subgraph polytope is 0-1).〔Bertrand Guenin, "A characterization of weakly bipartite graphs," ''Journal of Combinatorial Theory'', Series B, 83 (1): 112–168, 2001.〕〔 * * Satoru Iwata, Lisa Fleischer, Satoru Fujishige, and Alexander Schrijver for showing submodular minimization to be strongly polynomial.〔Satoru Iwata, Lisa Fleischer, Satoru Fujishige, "A combinatorial strongly polynomial algorithm for minimizing submodular functions," ''Journal of the ACM'', 48 (4): 761–777, 2001.〕〔Alexander Schrijver, "A combinatorial algorithm minimizing submodular functions in strongly polynomial time," ''Journal of Combinatorial Theory'', Series B 80 (2): 346–355, 2000.〕〔 * 2006: * * Manindra Agrawal, Neeraj Kayal and Nitin Saxena, for the AKS primality test.〔Manindra Agrawal, Neeraj Kayal and Nitin Saxena, "PRIMES is in P," ''Annals of Mathematics'', 160 (2): 781–793, 2004.〕〔.〕〔(2006 Fulkerson Prize citation ), retrieved 2012-08-19.〕 * * Mark Jerrum, Alistair Sinclair and Eric Vigoda, for approximating the permanent.〔Mark Jerrum, Alistair Sinclair and Eric Vigoda, "A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries," ''Journal of the ACM'', 51 (4): 671–697, 2004.〕〔 * * Neil Robertson and Paul Seymour, for the Robertson–Seymour theorem showing that graph minors form a well-quasi-ordering.〔Neil Robertson and Paul Seymour, "Graph Minors. XX. Wagner's conjecture," ''Journal of Combinatorial Theory'', Series B, 92 (2): 325–357, 2004.〕〔 * 2009: * * Maria Chudnovsky, Neil Robertson, Paul Seymour, and Robin Thomas, for the strong perfect graph theorem.〔Maria Chudnovsky, Neil Robertson, Paul Seymour, and Robin Thomas, "The strong perfect graph theorem", ''Annals of Mathematics'', 164: 51–229, 2006.〕〔(2009 Fulkerson Prize citation ), retrieved 2012-08-19.〕 * * Daniel A. Spielman and Shang-Hua Teng, for smoothed analysis of linear programming algorithms.〔Daniel A. Spielman and Shang-Hua Teng, "Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time", ''Journal of the ACM'' 51: 385–463, 2004.〕〔 * * Thomas C. Hales and Samuel P. Ferguson, for proving the Kepler conjecture on the densest possible sphere packings.〔Thomas C. Hales, "A proof of the Kepler conjecture", ''Annals of Mathematics'' 162: 1063–1183, 2005.〕〔Samuel P. Ferguson, "Sphere Packings, V. Pentahedral Prisms", ''Discrete and Computational Geometry'' 36: 167–204, 2006.〕〔 * 2012: * * Sanjeev Arora, Satish Rao, and Umesh Vazirani for improving the approximation ratio for graph separators and related problems from to .〔Sanjeev Arora, Satish Rao, and Umesh Vazirani, "Expander flows, geometric embeddings and graph partitioning", ''Journal of the ACM'' 56: 1-37, 2009.〕 * * Anders 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.〔Anders Johansson, Jeff Kahn, and Van H. Vu, "Factors in random graphs", ''Random Structures and Algorithms'' 33: 1-28, 2008.〕 * * László Lovász and Balázs Szegedy for characterizing subgraph multiplicity in sequences of dense graphs.〔László Lovász and Balázs Szegedy, "Limits of dense graph sequences", ''Journal of Combinatorial Theory'', Series B, 96: 933-957, 2006.〕 * 2015 : * *Francisco Santos Leal for a counter-example of the Hirsch conjecture.〔(2015 Fulkerson Prize citation ), retrieved 2015-07-18.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fulkerson Prize」の詳細全文を読む スポンサード リンク
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