Cyclic uniform 2-factorizations of the complete multipartite graph

2016/03/21 by Pasotti, Anita, Pellegrini, Marco Antonio
#05B30 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1603.06469

Abstract

The generalization of the Oberwolfach Problem, proposed by J. Liu in 2000, asks for a uniform 2-factorization of the complete multipartite graph K_{m× n}. Here we focus our attention on 2-factorizations regular under the cyclic group Z_mn, whose 2-factors are disjoint union of cycles all of even length ℓ. In particular, we present a complete solution for the extremal cases ℓ=4 and ℓ=mn.

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