Sharply Transitive $1$-Factorizations of Complete Multipartite Graphs

Giuseppe Mazzuoccolo, Gloria Rinaldi


Given a finite group $G$ of even order, which graphs $\Gamma$ have a $1$-factorization admitting $G$ as automorphism group with a sharply transitive action on the vertex-set? Starting from this question, we prove some general results and develop an exhaustive analysis when $\Gamma$ is a complete multipartite graph and $G$ is cyclic.

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