A Short Proof of a Theorem of Kano and Yu on Factors in Regular Graphs

In this note we present a short proof of the following result, which is a slight extension of a nice 2005 theorem by Kano and Yu. Let e be an edge of an rregular graph G. If G has a 1-factor containing e and a 1-factor avoiding e, then G has a k-factor containing e and a k-factor avoiding e for every k ∈ {1, 2, . . . , r−1}.

• Type: Journal
• Year: 2007
• Where: COMBINATORICS
• Authors: Lutz Volkmann
• Keywords: COMBINATORICS 2007, Rregular Graph G, Short Proof, Slight Extension