On the strong perfect graph conjecture | Zendy

Olariu Stephan | Zendy

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On the strong perfect graph conjecture

Author(s) -

Olariu Stephan

Publication year - 1988

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.3190120206

Subject(s) - combinatorics , mathematics , conjecture , perfect graph , graph , perfect graph theorem , trivially perfect graph , discrete mathematics , graph factorization , distance hereditary graph , line graph , graph power , voltage graph , pathwidth

A graph G is perfect if for every induced subgraph H of G the chromatic number χ( H ) equals the largest number ω( H ) of pairwise adjacent vertices in H . Berge's famous Strong Perfect Graph Conjecture asserts that a graph G is perfect if and only if neither G nor its complement G¯ contains an odd chordless cycle of length at least 5. Its resolution has eluded researchers for more than 20 years. We prove that the conjecture is true for a class of graphs that we describe by forbidden configurations.

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