Some new results on 1-rotational 2-factorizations of the complete graph

✍ Scribed by Tommaso Traetta

• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 129 KB
• Volume: 18
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.20241

✦ Synopsis

Abstract

It is known that a necessary condition for the existence of a 1‐rotational 2‐factorization of the complete graph K~2__n__+1~ under the action of a group G of order 2__n__ 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 4__t__+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