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21st Cumberland Conference on Graph Theory, Combinatorics, and Computing ---In Honor of Mike Plummer's 70th Birthday
May 15-17, 2008
Vanderbilt University
Nashville, TN, USA

Organizers
Mark Ellingham and Gexin Yu

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Star-uniform Graphs
by
Mikio Kano
Ibaraki University
Coauthors: Yunjian Wu and Qinglin Yu

A star-factor of a graph G is a spanning subgraph of G such that each of its components is a star. Clearly, every graph without isolated vertices has a star factor. A graph G is called star-uniform if all star-factors of G have the same number of components. To characterize star-uniform graphs was an open problem posed by Hartnell and Rall. We characterize all star-uniform graphs with minimum degree at least two. Our proof relies heavily on Gallai-Edmonds Matching Structure Theorem.

Date received: April 9, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawn-30.