Basic perfect graphs and their extensions

Zverovich, Igor E.; Zverovich, Vadim

Abstract

In this article, we present a characterization of basic graphs in terms of forbidden induced subgraphs. This class of graphs was introduced by Conforti et al. (Square-free perfect graphs, J. Combin. Theory Ser. B, 90 (2) (2004) 257-307), and it plays an essential role in the announced proof of the Strong Perfect Graph Conjecture by Chudnovsky et al. (http://arxiv.org/PS_cache/math/ pdf/0212/0212070.pdf). Let G and H be graphs. A substitution of H in G replacing a vertex v∈V(G) is the graph G(v→H) consisting of disjoint union of H and G-v with the additional edge-set {xy:x∈V(H),y∈NG(v)}. For a class of graphs P, its substitutional closure P* consists of all graphs that can be obtained from graphs of P by repeated substitutions. We apply the reducing pseudopath method (Discrete Appl. Math. 128 (2-3) (2003) 487-509) to characterize the substitutional closure of the class of basic graphs in terms of forbidden induced subgraphs. © 2005 Elsevier B.V. All rights reserved.

• Presentation Conference Type: Conference Paper (published)
• Publication Date: Apr 6, 2005
• Journal: Discrete Mathematics
• Print ISSN: 0012-365X
• Publisher: Elsevier
• Peer Reviewed: Not Peer Reviewed
• Volume: 293
• Issue: 1-3
• Pages: 291-311
• DOI: https://doi.org/10.1016/j.disc.2004.08.033
• Keywords: perfect graphs, basic graphs, line graphs, substitutional closure, forbidden induced subgraphs
• Public URL: https://uwe-repository.worktribe.com/output/1052179
• Publisher URL: http://dx.doi.org/10.1016/j.disc.2004.08.033