摘要
Alavi等人在[1]中定义了图的一种新分解,即升分解,并提出猜想:设G是星s_1,s_2,…,s_k的并图,s_i含有α_i条边,n≤α_i≤2n-2,sum form i=1 to k(α_i=),则G可升分解为星图的并。本文证明了出现下列条件之一时猜想成立。 1.α_1,α_2,…α_k中至少有k-2个α_i(1≤i≤k)相等; 2.max{α_i|i=1,2,…,k-1}-min{α_i|i=1,2,…,k-1}≤1。
A conjecture was posed by Alavi et. al concerning a new kind of subgraph decomposition, that is the ascending subgraph decomposition, as follows: Let n≥ 2 be an integer and G a union of stars with sizes ,where and G has size Then G has an ascending stars de-composition. In this paper we proved that the conjecture is true if one of the following conditions holds:1 . at least k-2 numbers in are equal;2 . max .
