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Distribution of Cycle Lengths in Graphs

✍ Scribed by Genghua Fan

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 148 KB
Volume: 84
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.2001.2071

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✦ Synopsis

Bondy and Vince proved that every graph with minimum degree at least three contains two cycles whose lengths differ by one or two, which answers a question raised by Erdo ˝s. By a different approach, we show in this paper that if G is a graph with minimum degree d(G) \ 3k for any positive integer k, then

To settle a problem proposed by Bondy and Vince, we obtain that if G is a nonbipartite 3-connected graph with minimum degree at least 3k for any positive integer k, then G contains 2k cycles of consecutive lengths m, m+1, ..., m+2k -1 for some integer m \ k+2.

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