关于群图的{C_(ni)|i∈I}—因子

On {C_(ni)|i ∈ I}-Factors of Group Graphs

设C_n是长度n(n≥3)的圈。如果G的生成子图F的每个分支都同构于圈C_(ni),i∈I之一,则F称为G的一个{C_(ni)|i∈I}一因子。若G是其边不相交的{C_(ni)_i∈I}一因子之并,则G称为可{C_(ni)|i∈I}因子化。1988年,M.—J.P.Ruiz在文中给出了有限简单连通无向群图C_n一因子的充分条件及可{C_a,C_b…C_p}一因子化的充分条件。本文把Ruiz的结果推广到一般的简单群图之中。

Let Cn denote the cycle of length n, n≥ 3. If each of components of a spanning subgraph F of a graph G is isomorphic toone of the cycle Cni, i ∈ I, then F is called a {Cni|i ∈ I)-factorsof G. G is a {Cni|i ∈ I}-factrable if it is the union of edge-disjoint {Cni |i ∈ I)-factors. In 1988,M. -J. P. Ruiz presented asufficient condition for a group graph to have a Gn-factor and a sufficient condition for agroup graph to be Cn -factorable. In this paper, we will generalize Ruiz’s results.