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

Paulusma, Daniel and Yoshimoto, K. (2008) 'Relative length of longest paths and longest cycles in triangle-free graphs.', Discrete mathematics., 308 (7). pp. 1222-1229.

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.

Item Type:Article
Keywords:Triangle-free graph, Cycle, Ore-condition, Relative length.
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1016/j.disc.2007.03.070
Publisher statement:NOTICE: this is the author's version of a work that was accepted for publication in Discrete mathematics.
Date accepted:No date available
Date deposited:07 October 2010
Date of first online publication:April 2008
Date first made open access:No date available

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