关于Abel群上Cayley图的Hamilton圈分解

On Hamiltonian Decomposition of Cayley Graphs of Abelian Groups

设Ｇ（Ｆ，Ｔ∪Ｔ￣（－１））是有限Ａｂｅｌ群Ｆ上的Ｃａｙｌｅｙ图，Ｔ∩Ｔ￣（－１）只含２阶元。此文证明了当Ｔ是Ｆ的极小生成元集时，若ｄ（Ｇ）＝２ｋ，则Ｇ是ｋ个边不相交的Ｈａｍｉｌｔｏｎ圈的并；若ｄ（Ｇ）＝２ｋ＋１，则Ｇ是ｋ个边不相交的Ｈａｍｉｌｔｏｎ圈与一个１－因子的并。

Let G(F,T∪T￣(-1)) be a Cayley graph of a finite abelian group F andeach element of T∩T￣(-1)be of order two. It has been showed in this paper thatwhen T is a minimal generating set of F,G can be decomposed into k edge-disjo-int Hamilton cycles ifd(G)=2k, or k edge-disjoint Hamilton cycles and a 1-factorif d(G)=2k+1.