Elsevier

Discrete Mathematics

Volume 309, Issue 14, 28 July 2009, Pages 4762-4771
Discrete Mathematics

Ore-type conditions implying 2-factors consisting of short cycles

Dedicated to Anthony Hilton
https://doi.org/10.1016/j.disc.2008.06.001Get rights and content
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Abstract

For every graph G, let σ2(G)=min{d(x)+d(y):xyE(G)}. The main result of the paper says that every n-vertex graph G with σ2(G)4n31 contains each spanning subgraph H all whose components are isomorphic to graphs in {K1,K2,C3,K4,C5+}. This generalizes the earlier results of Justesen, Enomoto, and Wang, and is a step towards an Ore-type analogue of the Bollobás–Eldridge–Catlin Conjecture.

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Degree conditions

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