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Cycle lengths in graphs with large minimum degree

✍ Scribed by V. Nikiforov; R. H. Schelp

Publisher: John Wiley and Sons
Year: 2006
Tongue: English
Weight: 114 KB
Volume: 52
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20151

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✦ Synopsis

Abstract

Our main result is the following theorem.

Let k ≥ 2 be an integer, G be a graph of sufficiently large order n, and δ(G) ≥ n/k. Then:

G contains a cycle of length t for every even integer t ∈ [4, δ(G) + 1].

If G is nonbipartite then G contains a cycle of length t for every odd integer t ∈ [2__k__ − 1, δ(G) + 1], unless k ≥ 6 and G belongs to a known exceptional class.

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