图中存在f-因子的度条件(英文)  

A degree condition for graphs to have f-factors

作　　者：李继猛[1] 

机构地区：[1]邵阳学院数学系,邵阳422004

出　　处：《湘潭大学自然科学学报》2005年第2期35-38,共4页Natural Science Journal of Xiangtan University

基　　金：国家自然科学基金资助项目(104711161)

摘　　要：设n≥3是一个整数,G是一个具有顶点集V(G)的图,并设f是定义在V(G)上的非负整值函数.设a=max{g(x) |x∈V(G)} ,b=min{f(x) |x∈V(G)} ,并有b,a≥2 ,n≥b/(a-1) +1 ,如果存在点v∈V(G)使得f(v)≡1 (mod 2) ,假定b≥n-1 .则每个连通的使得f(V(G))为偶数的K1 ,n-free图G有f-因子,如果它的最小度至少是(n-1)(b+1) +aab(n-1) +a2(n-1)-n-a1b(2n(-n-1)1 +)a2+n-3 .Let n≥3 be an integer and G be a graph. Let f(x) be an integer-valued function defined on V(G), and let a=min{f(x):x∈V(G)},b=max{f(x):x∈V(G)}, and b, a≥2, n≥a/(b-1)+1,if there is a vertex x∈V(G) such that f(x) odd, we assume that a≥n-1. We prove that every connected graph G with f(V(G)) even has an f-factor if it contains no K_1,n as an induced subgraph and its minimum degree is at least(n-1)(b+1)+aab(n-1)+a2(n-1)-n-1ab(n-1)+a2(n-1)2+n-3.

关 键 词：图 F-因子 度 

分 类 号：O157.58[理学—数学]