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A Generalization of the Perfect Graph Theorem Under the Disjunctive Index
Mathematics of Operations Research, 2002 In this paper, we relate antiblocker duality between polyhedra, graph theory, and the disjunctive procedure. In particular, we analyze the behavior of the disjunctive procedure over the clique relaxation, 𝒦(G), of the stable set polytope in a graph G, and the one associated to its complementary graph, 𝒦(Ḡ).
NĂ©stor E. Aguilera +2 more
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2020 International Conference on Computational Science and Computational Intelligence (CSCI), 2020 The strong perfect graph theorem is the proof of the famous Berge’s conjecture that the graph is perfect if and only if it is free of odd holes and odd anti-holes. The conjecture was settled after 40 years in 2002 by Maria Chudnovsky et. al. and the proof was published in 2006.
Maher Heal
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Acta Mathematicae Applicatae Sinica, English Series, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiao-fengGuo, YiHuang
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Tutte type theorems for graphs having a perfect internal matching
Information Processing Letters, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Miklós Bartha, Miklós Krész
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The Strong Perfect Graph Theorem for a Class of Partitionable Graphs
, 1984 A simple adjacency criterion is presented which, when satisfied, implies that a minimal imperfect graph is an odd hole or an odd antihole. For certain classes of graphs, including K 1,3 -free graphs, it is straightforward to validate this criterion and thus establish the Strong Perfect Graph Theorem for such graphs.
Rick Giles, L. E. Trotter, Alan Tucker
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A Homogeneousity Theorem for Perfect 1-Codes in Regular Graphs
, 1985 Kazumasa Nomura
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