Abstract

A graph G is called preperfect if each induced subgraph G′⊆G of order at least 2 has two vertices x, y such that either all maximum cliques of G′ containing x contain y, or all maximum independent sets of G′ containing y contain x, too. Giving a partial answer to a problem of Hammer and Maffray [Combinatorica 13 (1993), 199–208], we describe new classes of minimally non-preperfect graphs, and prove the following characterizations:

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