摘要
对图存在ｆ—因子涉及到独立数和最小度条件进行了研究，得到了下列结果：设ａ，ｂ为整数且ｂ≥ａ≥１，ｂ≥２，Ｇ是一个有ｎ个顶点的连通图且ｎ≥（ａ＋ｂ）２／ａ．ｆ（ｘ）是定义在Ｖ（Ｇ）上的非负整数函数，满足∑ｘ∈Ｖ（Ｇ）ｆ（ｘ）是偶数且ａ≤ｆ（ｘ）≤ｂ．如果Ｇ满足δ≥（ｂ－１）ｎ＋ａ＋ｂ－２ａ＋ｂ－１且δ＞（ｂ－２）ｎ＋２α－２ａ＋ｂ－２，则Ｇ存在ｆ－因子，其中δ和α分别表示图Ｇ的最小度和独立数．
A sufficient condition is given depending on the minimum degree and independence number of a graph for the existence of an f factor in a graph,which generalizes a result of T.Niessen on k factors.the following result is also proved:Lte a and b be integers with b ≥ a ≥1, b ≥2, G be a connected graph of order n with n≥(a+b) 2a ,and f an integer-valued functiondefined on V(G) such that a≤f(x)≤b and ∑x∈E(G)f(x)≡0 (mod2).Suppose that G satisfies δ≥(b-1)n+a+b-2a+b-1 and δ>(b-2)n+2a-2a+b-2 ,then G has a factor.
出处
《山东师范大学学报（自然科学版）》
CAS
1997年第1期12-16,共5页
Journal of Shandong Normal University(Natural Science)
关键词
图论
F-因子
独立数
最小度
简单图
graph
factor
f factor
independence number
minimum degree
