Heavy cycles passing through some specified vertices in weighted graphs

Jun Fujisawa, Kiyoshi Yoshimoto, Shenggui Zhang

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

A weighted graph is one in which every edge e is assigned a nonnegative number, called the weight of e. The sum of the weights of the edges incident with a vertex v is called the weighted degree of v. The weight of a cycle is defined as the sum of the weights of its edges. In this paper, we prove that: (1) if G is a 2-connected weighted graph such that the minimum weighted degree of G is at least d, then for every given vertices x and y, either G contains a cycle of weight at least 2d passing through both of x and y or every heaviest cycle in G is a hamiltonian cycle, and (2) if G is a 2-connected weighted graph such that the weighted degree sum of every pair of nonadjacent vertices is at least s, then for every vertex y, G contains either a cycle of weight at least s passing through y or a hamiltonian cycle. AMS classification: 05C45 05C38 05C35.

Original languageEnglish
Pages (from-to)93-103
Number of pages11
JournalJournal of Graph Theory
Volume49
Issue number2
DOIs
Publication statusPublished - 2005 Jun

Fingerprint

Weighted Graph
Cycle
Hamiltonian circuit
Connected graph
Degree Sum
Vertex of a graph
Weighted Sums
Non-negative

Keywords

  • (Heavy, hamiltonian) cycle
  • (Weighted) degree sum
  • Minimum (weighted) degree
  • Weighted graph

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Heavy cycles passing through some specified vertices in weighted graphs. / Fujisawa, Jun; Yoshimoto, Kiyoshi; Zhang, Shenggui.

In: Journal of Graph Theory, Vol. 49, No. 2, 06.2005, p. 93-103.

Research output: Contribution to journalArticle

Fujisawa, Jun ; Yoshimoto, Kiyoshi ; Zhang, Shenggui. / Heavy cycles passing through some specified vertices in weighted graphs. In: Journal of Graph Theory. 2005 ; Vol. 49, No. 2. pp. 93-103.
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