On heavy paths in 2-connected weighted graphs

TL;DR

This paper establishes new weighted degree conditions that guarantee the existence of heavy or Hamilton paths with specified end-vertices in 2-connected weighted graphs, advancing understanding of path structures under weight constraints.

Contribution

It introduces three novel weighted degree criteria for ensuring heavy or Hamilton paths with fixed end-vertices in 2-connected weighted graphs.

Findings

Three weighted degree conditions for heavy or Hamilton paths

Conditions applicable to graphs with specified end-vertices

Results extend previous unweighted path theorems

Abstract

A weighted graph is a graph in which every edge is assigned a non-negative real number. In a weighted graph, the weight of a path is the sum of the weights of its edges, and the weighed degree of a vertex is the sum of the weights of the edges incident with it. In this paper we give three weighted degree conditions for the existence of heavy or Hamilton paths with one or two given end-vertices in 2-connected weighted graphs.