Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/24993
Title: An Implicit Weighted Degree Condition for Heavy Cycles in Weighted Graphs
Authors: Chen, B
Zhang, S
Cheng, TCE 
Issue Date: 2007
Publisher: Springer
Source: Lecture notes in computer science (including subseries Lecture notes in artificial intelligence and lecture notes in bioinformatics), 2007, v. 4381 LNCS, p. 21-29 How to cite?
Journal: Lecture notes in computer science (including subseries Lecture notes in artificial intelligence and lecture notes in bioinformatics) 
Abstract: Let G be a 2-connected weighted graph and m a nonnegative number. As introduced by Li as the weighted analogue of a concept due to Zhu et al, we use id w (v) to denote the implicit weighted degree of a vertex v in G. In this paper we prove that G contains either a Hamilton cycle or a cycle of weight at least m, if the following two conditions are satisfied: (1) max {id w (u), id w (v)}≥ m/2 for each pair of nonadjacent vertices u and v that are vertices of an induced claw or an induced modified claw of G; (2) In each induced claw, each induced modified claw and each induced P 4 of G, all the edges have the same weight. This is a common generalization of several previous results on the existence of long cycles in unweighted graphs and heavy cycles in weighted graphs.
Description: 7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005, Xi'an, 22-24 November 2005
URI: http://hdl.handle.net/10397/24993
ISBN: 3540706658
9783540706656
ISSN: 0302-9743
EISSN: 1611-3349
DOI: 10.1007/978-3-540-70666-3_3
Appears in Collections:Conference Paper

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