A Class of Perfect Graphs

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1982 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Algebraic Discrete Methods, volume 3, pages 281-284 (issn: 0196-5212, eissn: 2168-345X,

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Authors: Shearer, James B.;

doi: 10.1137/0603027

A Class of Perfect Graphs

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Abstract

Let P be a simply connected polyomino. Let $G( P )$ be the graph whose vertices are the maximal rectangles in P, two such vertices being adjacent if the corresponding rectangles have nontrivial intersection. In this paper we show that $G ( P )$ is perfect. This solves a problem posed by Berge et al.

Keywords

Coloring of graphs and hypergraphs, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), simply connected polyomino, Polyominoes, perfect graph, maximal rectangles, Combinatorial aspects of packing and covering

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