Weighted degrees and heavy cycles in weighted graphs

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3 Citations (Scopus)

Abstract

A weighted graph is a graph provided with an edge-weighting functionw from the edge set to nonnegative real numbers. Bondy and Fan [Annals of Discrete Math. 41 (1989), 53-69] began the study on the existence of heavy cycles in weighted graphs. Though several results with Dirac-type degree condition can be generalized to an Ore-type one in unweighted graphs, it is shown in Bondy et al. [Discuss. Math. Graph Theory 22 (2002), 7-15] that Bondy and Fan's theorem, which uses Dirac-type condition, cannot be generalized analogously by using Ore-type condition. In this paper we investigate the property peculiar to weighted graphs, and prove a theorem on the existence of heavy cycles in weighted graphs under an Ore-type condition, which generalizes Bondy and Fan's theorem. Moreover, we show the existence of heavy cycles passing through some specified vertices.

Original languageEnglish
Pages (from-to)6483-6495
Number of pages13
JournalDiscrete Mathematics
Volume309
Issue number23-24
DOIs
Publication statusPublished - 2009 Dec 6
Externally publishedYes

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Keywords

  • Heavy cycle
  • Weighted degree
  • Weighted graph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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