Article ID Journal Published Year Pages File Type
419485 Discrete Applied Mathematics 2011 7 Pages PDF
Abstract

We consider minimal 1-factor covers of regular multigraphs, focusing on those that are 1-factorizations. In particular, we classify cubic graphs such that every minimal 1-factor cover is also a 1-factorization, and also classify simple regular bipartite graphs with this property. For r>3r>3, we show that there are finitely many simple rr-regular graphs such that every minimal 1-factor cover is also a 1-factorization.

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Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
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1-factor covers of regular graphs
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