Heavy cycles passing through some specified vertices in weighted graphs

Jun Fujisawa, Kiyoshi Yoshimoto, Shenggui Zhang

研究成果: Article査読

5 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)93-103
ページ数11
ジャーナルJournal of Graph Theory
49
2
DOI
出版ステータスPublished - 2005 6

ASJC Scopus subject areas

  • 幾何学とトポロジー

フィンガープリント

「Heavy cycles passing through some specified vertices in weighted graphs」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル