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Staruniform Graphs  Mikio Kano
; Yunjian Wu
; Qinglin Yu
;  Date: 
2 Jul 2007  Abstract:  A {it starfactor} of a graph $G$ is a spanning subgraph of $G$ such that
each of its component is a star. Clearly, every graph without isolated vertices
has a star factor. A graph $G$ is called {it staruniform} if all starfactors
of $G$ have the same number of components. To characterize staruniform 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 factorcriticality and domination number to characterize all
staruniform graphs with the minimum degree at least two. Our proof is heavily
relied on GallaiEdmonds Matching Structure Theorem.  Source:  arXiv, arxiv.0707.0226  Services:  Forum  Review  PDF  Favorites 


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