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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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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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