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A decomposition for strongly perfect graphs
Author(s) -
Olariu Stephan
Publication year - 1989
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.3190130305
Subject(s) - combinatorics , mathematics , disjoint sets , cograph , partition (number theory) , graph , split graph , induced subgraph , induced path , modular decomposition , decomposition , discrete mathematics , distance hereditary graph , chordal graph , pathwidth , line graph , 1 planar graph , graph power , chemistry , organic chemistry , vertex (graph theory)
A graph G is strongly perfect if every induced subgraph H of G contains a stable set that meets all the maximal cliques of H. We present a graph decomposition that preserves strong perfection: more precisely, a stitch decomposition of a graph G = (V, E) is a partition of V into nonempty disjoint subsets V 1 , V 2 such that in every P 4 with vertices in both V i apos;s, each of the three edges has an endpoint in V 1 and the other in V 2 . We give a good characterization of graphs that admit a stitch decomposition and establish several results concerning the stitch decomposition of strongly perfect graphs.