Abstract
AbstractA 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 V1, V2 such that in every P4 with vertices in both Viapos;s, each of the three edges has an endpoint in V1 and the other in V2.We give a good characterization of graphs that admit a stitch decomposition and establish several results concerning the stitch decomposition of strongly perfect graphs.
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