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Cyclic Perfect One Factorizations of K2n

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DOI: 10.1016/s0304-0208(08)72892-5

Abstract

Abstract Recently Hartman and Rosa characterized those n for which K2n admits a cyclic one factorization. We show that K2n admits a cyclic perfect one factorization if and only if n is prime. We also show that if n is prime there is a one to one, onto correspondence between cyclic perfect one factorizations on K2n and starter induced perfect one factorizations on Kn+1. Moreover the full symmetry group of the cyclic perfect one factorization is that of the corresponding starter induced perfect one factorization direct sum Z2

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