Document Type

Article

Publication Date

1990

DOI

10.1016/0012-365x(90)90248-g

Publication Title

Discrete Mathematics

Volume

80

Issue

3

Pages

281-296

Abstract

An edge uv of a graph G is called a wing if there exists a chordless path with vertices u, v, x, y and edges uv, vx, xy. The wing-graph W(G) of a graph G is a graph having the same vertex set as G; uv is an edge in W(G) if and only if uv is a wing in G. A graph G is saturated if G is isomorphic to W(G). A star-cutset in a graph G is a non-empty set of vertices such that G — C is disconnected and some vertex in C is adjacent to all the remaining vertices in C. V. Chvátal proposed to call a graph unbreakable if neither G nor its complement contain a star-cutset. We establish several properties of unbreakable graphs using the notions of wings and saturation. In particular, we obtain seven equivalent versions of the Strong Perfect Graph Conjecture.

Comments

Elsevier open archive. Copyright © 1990 Published by Elsevier B.V. All rights reserved.

Original Publication Citation

Olariu, S. (1990). Wings and perfect graphs. Discrete Mathematics, 80(3), 281-296. doi:10.1016/0012-365x(90)90248-g

ORCID

0000-0002-3776-216X (Olariu)

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