A graph is balanced if its clique-vertex incidence matrix contains no square submatrix of odd order with exactly two ones per row and per column. There is a characterization of balanced graphs by forbidden induced subgraphs, but no characterization by mininal forbidden induced subgraphs is known, not even for the case of circular-arc graphs. A circular-arc graph is the intersection graph of a family of arcs on a circle. In this work, we characterize when a given graph G is balanced in terms of minimal forbidden induced subgraphs, by restricting the analysis to the case where G belongs to certain classes of circular-arc graphs, including Helly circular-arc graphs, claw-free circular-arc graphs, and gem-free circular-arc graphs. In the case of gem-free circular-arc graphs, analogous characterizations are derived for two superclasses of balanced graphs: clique-perfect graphs and coordinated graphs.

Source : oai:HAL:hal-01188914v1

Volume: Vol. 16 no. 3 (in progress)

Section: Graph Theory

Published on: June 18, 2014

Submitted on: March 13, 2013

Keywords: balanced graphs,clique-perfect graphs,circular-arc graphs,coordinated graphs,perfect graphs,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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