Interval bigraphs and circular arc graphs

Authors:
Pavol Hell;Jing Huang
Affiliations:
School of Computing Science, Simon Fraser University, Burnaby, B.C., Canada, V5A 1S6;Department of Mathematics and Statistics, University of Victoria, P.O. Box 3045, Victoria, B.C., Canada, V8W 3P4
Venue:
Journal of Graph Theory
Year:
2004

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Abstract

We prove that the complements of interval bigraphs are precisely those circular arc graphs of clique covering number two, which admit a representation without two arcs covering the whole circle. We give another characterization of interval bigraphs, in terms of a vertex ordering, that we hope may prove helpful in finding a more efficient recognition algorithm than presently known. We use these results to show equality, amongst bipartite graphs, of several classes of structured graphs (proper interval bigraphs, complements of proper circular arc graphs, asteroidal-triple-free graphs, permutation graphs, and co-comparability graphs). Our results verify a conjecture of Lundgren and disprove a conjecture of Müller. © 2004 Wiley Periodicals, Inc. J Graph Theory 46: 313–327, 2004