Uniformly Weighted Star-Factors of Graphs

Details Uniformly Weighted Star-Factors of Graphs Uniformly Weighted Star-Factors of Graphs

2007-07-02

arxiv.org/abs/0707.0227v1

Mathematics

Combinatorics

Scientific paper

A {\it star-factor} of a graph $G$ is a spanning subgraph of $G$ such that each component of which is a star. An {\it edge-weighting} of $G$ is a function $w: E(G)\longrightarrow \mathbb{N}^+$, where $\mathbb{N}^+$ is the set of positive integers. Let $\Omega$ be the family of all graphs $G$ such that every star-factor of $G$ has the same weights under a fixed edge-weighting $w$. In this paper, we present a simple structural characterization of the graphs in $\Omega$ that have girth at least five.

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