On cover-structure graphs

Authors:
Henning Wunderlich
Affiliations:
Universität Ulm, Fakultät für Ingenieurwissenschaften und Informatik, Institut für Theoretische Informatik, Oberer Eselsberg, 89069 Ulm, Germany
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

Motivated by a problem in communication complexity, we study cover-structure graphs (cs-graphs), defined as intersection graphs of maximal monochromatic rectangles in a matrix. We show that not every graph is a cs-graph. Especially, squares and odd holes are not cs-graphs. It is natural to look at graphs (beautiful graphs) having the property that each induced subgraph is a cs-graph. They form a new class of Berge graphs. We make progress towards their characterization by showing that every square-free bipartite graph is beautiful, and that beautiful line graphs of square-free bipartite graphs are just Path-or-Even-Cycle-of-Cliques graphs.