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{\bf Mathieu Bogaerts and Giuseppe Mazzuoccolo}
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{\bf Cyclic and Dihedral 1-Factorizations of Multipartite Graphs}
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An automorphism group $G$ of a $1$-factorization of the complete multipartite graph $K_{m\times n}$ consists of permutations of the vertices of the graph mapping factors to factors. In this paper, we give a complete answer to the existence problem of a $1$-factorization of $K_{m\times n}$ admitting a cyclic or dihedral group acting sharply transitively on  the vertices of the graph.

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