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Circular choosability of graphs

✍ Scribed by Xuding Zhu

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 105 KB
Volume: 48
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20051

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✦ Synopsis

This paper discusses the circular version of list coloring of graphs. We give two definitions of the circular list chromatic number (or circular choosability) c;l ðGÞ of a graph G and prove that they are equivalent. Then we prove that for any graph G, c;l ðGÞ ! l ðGÞ À 1. Examples are given to show that this bound is sharp in the sense that for any > 0, there is a graph G with c;l ðGÞ < l ðGÞ À 1 þ . It is also proved that k-degenerate graphs G have c;l ðGÞ 2k. This bound is also sharp: for each > 0, there is a k-degenerate graph G with c;l ðGÞ ! 2k À . This shows that c;l ðGÞ could be arbitrarily larger than l ðGÞ. Finally we prove that if G has maximum degree k, then c;l ðGÞ k þ 1.

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