A characterization of triangle-free tolerance graphs

Authors:
Arthur H. Busch
Affiliations:
Department of Mathematics, University of Colorado at Denver, Denver, CO 80217, USA
Venue:
Discrete Applied Mathematics
Year:
2006

Citing 1
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Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms

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Abstract

We prove that a triangle-free graph G is a tolerance graph if and only if there exists a set of consecutively ordered stars that partition the edges of G. Since tolerance graphs are weakly chordal, a tolerance graph is bipartite if and only if it is triangle-free. We, therefore, characterize those tolerance graphs that are also bipartite. We use this result to show that in general, the class of interval bigraphs properly contains tolerance graphs that are triangle-free (and hence bipartite).