✦ LIBER ✦

Interval bigraphs and circular arc graphs

✍ Scribed by Pavol Hell; Jing Huang

Publisher: John Wiley and Sons
Year: 2004
Tongue: English
Weight: 130 KB
Volume: 46
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20006

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✦ Synopsis

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

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