Abstract
A graph G is called Berge if neither G nor its complement contains a chordless cycle with an odd number of nodes. The famous Berge’s Strong Perfect Graph Conjecture asserts that every Berge graph is perfect. A chair is a graph with nodes {a, b, c, d, e} and edges {ab, bc, cd}, eb. We prove that a Berge graph with no induced chair (chair-free) is perfect or, equivalently, that the Strong Perfect Graph Conjecture is true for chair-free graphs.
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This work was partially supported by MURST, Roma, Italy and Progetto Finalizzato Trasporti II, CNR, Italy
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Sassano, A. Chair-Free Berge Graphs Are Perfect. Graphs and Combinatorics 13, 369–395 (1997). https://doi.org/10.1007/BF03353015
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DOI: https://doi.org/10.1007/BF03353015