Abelian 1-factorizations of complete multipartite graphs
Abstract
An automorphism group G of a 1-factorization of the complete multipartite graph Km× n consists in permutations of the vertices of the graph mapping factors to factors. In this paper, we give a complete answer to the existence or non-existence problem of a 1-factorization of Km× n admitting an abelian group acting sharply transitively on the vertices of the graph.
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