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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
Maria Chudnovsky +2 more
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The Flat Wall Theorem for Bipartite Graphs with Perfect Matchings
Trends in Mathematics, 2021 Matching minors are a specialised version of minors fit for the study of graphs with perfect matchings. The first major appearance of matching minors was in a result by Little who showed that a bipartite graph is Pfaffian if and only if it does not contain \(K_{3,3}\) as a matching minor.
Archontia C. Giannopoulou
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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 ...
B Reed
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A weak box-perfect graph theorem
Journal of Combinatorial Theory Series BzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Roland Grappe
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Anticoncentration of Random Vectors via the Strong Perfect Graph Theorem
CombinatoricaIn 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 ...
Tomas Juskevicius, Valentas Kurauskas
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Perfect Matching in Random Graphs is as Hard as Tseitin [PDF]
TheoretiCS, 2022 We study the complexity of proving that a sparse random regular graph on an odd number of vertices does not have a perfect matching, and related problems involving each vertex being matched some pre-specified number of times.
Per Austrin, Kilian Risse
doaj +1 more source
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
openaire +3 more sources
An Even 2-Factor in the Line Graph of a Cubic Graph
Theory and Applications of Graphs, 2022 An even 2-factor is one such that each cycle is of even length. A 4- regular graph G is 4-edge-colorable if and only if G has two edge-disjoint even 2- factors whose union contains all edges in G.
SeungJae Eom, Kenta Ozeki
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An Ore-type Theorem for Perfect Packings in Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2009 We say that a graph G has a perfect H-packing (also called an H-factor) if there exists a set of disjoint copies of H in G which together cover all the vertices of G. Given a graph H, we determine, asymptotically, the Ore-type degree condition which ensures that a graph G has a perfect H-packing.
Daniela Kühn +2 more
openaire +3 more sources