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## Relative length of longest paths and longest cycles in triangle-free graphs. \ud

### Abstract

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
Journal:

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