【摘要】 本文使用A. Kotzig引进的分划广群的概念证明了关于完全图循环分解的下列结果。 1.如n为奇数,s为正整数,则完全图K_ns可以分解成边相离的长为n的循环的和。 2.如n₁,n₂,…,n_k为奇数n的所有异于1的正因子,则K_n可以分解成边相离的长为n₁,n₂,…,nk的循环的和。 3.如K_m可以分解成边相离的长为h的循环的和,K_n可以分解为边相离的长为k的循环的和,则K_mn可以分解成边相离的长为h,k,d的循环的和。其中d是h与k的最小公倍数。更多还原

【Abstract】 By using the operation of partition groupoids introduced by A. Kotzig, this paper gave some results about the cyclic decomposition of complete graphs. The main results in this paper are as follows. （1）If n is odd, s is a positive integer, then K_n s can be decomposed into the union of edge-disjoint cycles each with length n. （2）If n is odd and its positive factors are n₁, n₂, …, n_k besides 1, then K_n can be decomposed into the union of edge-disjoins cycles with lengths n₁, n₂, …, n_k. （3）If K_m and K_n can be decomposed into edge-disjoint cycles each with length h and k respectively, then K_ma can be decomposed into edge-disjoint cycles with lengths h, k and d; here d is the least common multiple of h and k.更多还原