### 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 |
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Pages (from-to) | 100-109 |

Number of pages | 10 |

Journal | Discrete Mathematics |

Volume | 300 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 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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## Cite this

*Discrete Mathematics*,

*300*(1-3), 100-109. https://doi.org/10.1016/j.disc.2005.06.006