Star-uniform Graphs
Combinatorics
2007-07-03 v1
Abstract
A {\it star-factor} of a graph is a spanning subgraph of such that each of its component is a star. Clearly, every graph without isolated vertices has a star factor. A graph is called {\it star-uniform} if all star-factors of have the same number of components. To characterize star-uniform graphs was an open problem posed by Hartnell and Rall, which is motivated by the minimum cost spanning tree and the optimal assignment problems. We use the concepts of factor-criticality and domination number to characterize all star-uniform graphs with the minimum degree at least two. Our proof is heavily relied on Gallai-Edmonds Matching Structure Theorem.
Cite
@article{arxiv.0707.0226,
title = {Star-uniform Graphs},
author = {Mikio Kano and Yunjian Wu and Qinglin Yu},
journal= {arXiv preprint arXiv:0707.0226},
year = {2007}
}