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Convex-round graphs are circular-perfect

✍ Scribed by Jørgen Bang-Jensen; Jing Huang

Publisher: John Wiley and Sons
Year: 2002
Tongue: English
Weight: 119 KB
Volume: 40
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.10047

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✦ Synopsis

Abstract

We show a connection between two concepts that have hitherto been investigated separately, namely convex‐round graphs and circular cliques. The connections are twofold. We prove that the circular cliques are precisely the cores of convex‐round graphs; this implies that convex‐round graphs are circular‐perfect, a concept introduced recently by Zhu [10]. Secondly, we characterize maximal K~r~‐free convex‐round graphs and show that they can be obtained from certain circular cliques in a simple fashion. Our proofs rely on several structural properties of convex‐round graphs. © 2002 Wiley Periodicals, Inc. J Graph Theory 40: 182–194, 2002

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