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In this paper, we study triangle-free graphs. Let G=(V,E) be an arbitrary triangle-free graph with minimum degree at least two and σ4(G)|V(G)|+2. We first show that either for any path P in G there exists a cycle C such that |VPVC|1, or G is isomorphic to exactly one exception. Using this result, we show that for any set S of at most δ vertices in G there is a cycle C such that SVC.\ud \u

Topics:
Triangle-free graph, Cycle, Ore-condition, Relative length.

Publisher: Elsevier

Year: 2008

DOI identifier: 10.1016/j.disc.2007.03.070

OAI identifier:
oai:dro.dur.ac.uk.OAI2:7425

Provided by:
Durham Research Online

Downloaded from
http://dro.dur.ac.uk/7425/1/7425.pdf

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