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We consider one–factorizations of complete graphs which possess an automorphism group fixing k ≥ 0 vertices and acting regularly (i.e., sharply transitively) on the others. Since the cases k = 0 and k = 1 are well known in literature, we study the case k≥ 2 in some detail. We prove that both k and the order of the group are even and the group necessarily contains k − 1 involutions. Constructions for...
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