完全图对于林的同构分解

Isomorphic Decomposition of Complete Graphs into Forests

F.Harary 等人[1]提出图的同构分解的若干未解决问题之一:问题(1.4) 刻划集合Kp/t中的林。本文研究了上述问题,获得如下结果: 定理若F是含k条边的无孤立点的毛虫林,且k|n(k是n的约数),则F∈K_(2n+1),F∈K_(2n)/(2n-1)。

F. Harary et al.posed the following unsolved problem; (1,4) characterize the forests in K_P/t. The author studied the problem for caterpillar forests, and obtained the following result: Theorem If F is a caterpillar forest of size k without isolated vertices, n=kd, then F∈K_(2n)/d(2n-1), F∈K_(2n+1)/d (2n+l).