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The strong perfect graph theorem [PDF]
Annals of Mathematics, 2006 A graph G is perfect if for every induced subgraph H, the chromatic number of H equals the size of the largest complete subgraph of H, and G is Berge if no induced subgraph of G is an odd cycle of length at least 5 or the complement of one. The "strong perfect graph conjecture" (Berge, 1961) asserts that a graph is perfect if and only if it is Berge. A
Robin Thomas +3 more
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A constructive formalization of the weak perfect graph theorem [PDF]
Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs, 2020 The 9th ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP 2020)
Abhishek Kr Singh, Raja Natarajan
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Anticoncentration of Random Vectors via the Strong Perfect Graph Theorem
Combinatorica, 2023 In this paper we give anticoncentration bounds for sums of independent random vectors in finite-dimensional vector spaces. In particular, we asymptotically establish a conjecture of Leader and Radcliffe (1994) and a question of Jones (1978). The highlight of this work is an application of the strong perfect graph theorem by Chudnovsky, Robertson ...
Juškevičius, Tomas +1 more
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Cyclewidth and the Grid Theorem for Perfect Matching Width of Bipartite Graphs [PDF]
International Workshop on Graph-Theoretic Concepts in Computer Science, 2019 A connected graph G is called matching covered if every edge of G is contained in a perfect matching. Perfect matching width is a width parameter for matching covered graphs based on a branch decomposition. It was introduced by Norine and intended as a tool for the structural study of matching covered graphs, especially in the context of Pfaffian ...
Hatzel, Meike +2 more
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Towards a Constructive Formalization of Perfect Graph Theorems [PDF]
Indian Conference on Logic and Its Applications, 2019 ICLA ...
Raja Natarajan, Abhishek Kr Singh
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A semi-strong Perfect Graph theorem
Journal of Combinatorial Theory, Series B, 1987 The perfectness of a graph G was defined by Berge in 1961. He also proposed the following two conjectures: (1) G is perfect if and only if it contains no induced subgraph isomorphic to an odd cycle of length greater than three or the complement of such a cycle (strong perfect graph conjecture) and (2) G is perfect if and only if \(\bar G\) is perfect ...
Bruce Reed
semanticscholar +5 more sources
A weak box-perfect graph theorem
Journal of Combinatorial Theory, Series Bnon ; non ; recherche ...
Patrick Chervet, Roland Grappe
semanticscholar +3 more sources
Note On: N. E. Aguilera, M. S. Escalante, G. L. Nasini, “A Generalization of the Perfect Graph Theorem Under the Disjunctive Index” [PDF]
Mathematics of Operations Research, 2003 We give short elementary proofs of two results by N. E. Aguilera, M. S. Escalante, and G. L. Nasini on the disjunctive index of the clique relaxation of the stable set polytope.
Gerards, A.H. +2 more
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The strong perfect graph theorem [PDF]
100 Years of Math Milestones, 2019 In 1960 Berge came up with the concept of perfect graphs, and in doing so, conjectured some characteristics about them. A perfect graph is a graph in which the chromatic number of every induced subgraph equals the size of the largest clique of that ...
Stephan Ramon Garcia, Steven Miller
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