2007/07/02 by Yunjian Wu, Wu, Yunjian, Qinglin Yu +1
Mathematics · #05C69 #05C70 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C69 #msc:05C70
paper · pdf · doi:10.48550/arxiv.0707.0227
arxiv created 2007/07/02 · arxiv updated 2009/12/01
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 ℕ+, where ℕ+ is the set of positive integers. Let Ω 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 Ω that have girth at least five.