Some new results on 1‐rotational 2‐factorizations of the complete graph |
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Authors: | Tommaso Traetta |
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Institution: | Dipartimento di Matematica e Informatica, Universitá degli Studi di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy |
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Abstract: | It is known that a necessary condition for the existence of a 1‐rotational 2‐factorization of the complete graph K2n+1 under the action of a group G of order 2n is that the involutions of G are pairwise conjugate. Is this condition also sufficient? The complete answer is still unknown. Adapting the composition technique shown in Buratti and Rinaldi, J Combin Des, 16 (2008), 87–100, we give a positive answer for new classes of groups; for example, the groups G whose involutions lie in the same conjugacy class and having a normal subgroup whose order is the greatest odd divisor of |G|. In particular, every group of order 4t+2 gives a positive answer. Finally, we show that such a composition technique provides 2‐factorizations with a rich group of automorphisms. © 2009 Wiley Periodicals, Inc. J Combin Designs 18: 237–247, 2010 |
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Keywords: | complete graph 1‐rotational 2‐factorization permutation group |
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