# 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 language English 100-109 10 Discrete Mathematics 300 1-3 https://doi.org/10.1016/j.disc.2005.06.006 Published - 2005 Sep 6

### Fingerprint

Degree Condition
Weighted Graph
Ores
Path
Hamilton Path
Join
Connected graph
Non-negative
Distinct
Sufficient Conditions
Vertex of a graph

### Keywords

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

### ASJC Scopus subject areas

• Discrete Mathematics and Combinatorics
• Theoretical Computer Science

### Cite this

In: Discrete Mathematics, Vol. 300, No. 1-3, 06.09.2005, p. 100-109.

Research output: Contribution to journalArticle

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