A Fan Type Condition For Heavy Cycles in Weighted Graphs

@article{Zhang2002AFT,
title={A Fan Type Condition For Heavy Cycles in Weighted Graphs},
author={Shenggui Zhang and Hajo Broersma and Xueliang Li and Ligong Wang},
journal={Graphs and Combinatorics},
year={2002},
volume={18},
pages={193-200}
}

A weighted graph is a graph in which each edge e is assigned a non-negative number w(e), called the weight of e. The weight of a cycle is the sum of the weights of its edges. The weighted degree d(v) of a vertex v is the sum of the weights of the edges incident with v. In this paper, we prove the following result: Suppose G is a 2-connected weighted graph which satisfies the following conditions: 1. max{dw(x), d(y) | d(x, y) = 2} ≥ c/2; 2. w(xz) = w(yz) for every vertex z ∈ N(x) ∩N(y) with d(x… CONTINUE READING