Claw conditions for heavy cycles in weighted graphs

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5 Citations (Scopus)

Abstract

A graph is called a weighted graph when each edge e is assigned a nonnegative number w(e), called the weight of e. For a vertex v of a weighted graph, d w (v) is the sum of the weights of the edges incident with v. For a subgraph H of a weighted graph G, the weight of H is the sum of the weights of the edges belonging to H. In this paper, we give a new sufficient condition for a weighted graph to have a heavy cycle. A 2-connected weighted graph G contains either a Hamilton cycle or a cycle of weight at least c, if G satisfies the following conditions: In every induced claw or induced modified claw F of G, (1) max{d w (x),d w (y)}≤ c/2 for each non-adjacent pair of vertices x and y in F, and (2) all edges of F have the same weight.

Original languageEnglish
Pages (from-to)217-229
Number of pages13
JournalGraphs and Combinatorics
Volume21
Issue number2
DOIs
Publication statusPublished - 2005 Jun 1

Keywords

  • Claw
  • Fan-type condition
  • Heavy cycle
  • Modified claw
  • Weighted graph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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