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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.