Ore-type degree condition for heavy paths in weighted graphs

Hikoe Enomoto, Jun Fujisawa, Katsuhiro Ota

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

A weighted graph is one in which every edge e is assigned a nonnegative number w(e), called the weight of e. For a vertex v of a weighted graph, dw(v) is the sum of the weights of the edges incident to v. And the weight of a path is the sum of the weights of the edges belonging to it. In this paper, we give a sufficient condition for a weighted graph to have a heavy path which joins two specified vertices. Let G be a 2-connected weighted graph and let x and y be distinct vertices of G. Suppose that dw(u)+dw(v)≥2d for every pair of non-adjacent vertices u and v∈V(G)\{x,y}. Then x and y are joined by a path of weight at least d, or they are joined by a Hamilton path. Also, we consider the case when G has some vertices whose weighted degree are not assumed.

Original languageEnglish
Pages (from-to)100-109
Number of pages10
JournalDiscrete Mathematics
Volume300
Issue number1-3
DOIs
Publication statusPublished - 2005 Sep 6

Keywords

  • Heavy path
  • Ore-type degree condition
  • Weighted graph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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