摘要
提出了完全图最小圈覆盖的覆盖数下界,运用递归构造的方法,把顶点数v的研究范围归结到区间[m,3m-1]中的部分数值上来,并就圈长m=6,8的情形给出了完全解.
A covering of the complete graph, Kv, by m-cycles（cycles of length m） , is a pair （V, F） where V is the vertex set of Kv, and F is a collection of m-cycles such that any edge of Kv occurs in at least one cycle of F. The most important problem of cycle coverings of complete graph is to confirm the cycles＇ number of the minimum coverings. In this paper, the infimum of cycle covering of the complete graph is supposed. And then, reduced the problem to the case where vertex v is intervenient of m and 3m-1. In particular, for m=6, 8 and all integers v≥m, the problems is solved completely.
出处
《山东理工大学学报（自然科学版）》
CAS
2008年第4期15-18,共4页
Journal of Shandong University of Technology:Natural Science Edition
关键词
组合数学
递归构造
完全图
覆盖
圈覆盖
combinatorics
recursive construct
complete graph
coverings
cycle coverings
