分数因子存在的两个充分条件  

The Sufficient Conditions for the Existence of Fractional Fa ctors Graphs

作　　者：李建湘[1] 邓汉元[2] 

机构地区：[1]湘潭工学院数理系,中国湘潭411201 [2]湖南师范大学数学与计算机科学学院数学系,中国长沙410081

出　　处：《湖南师范大学自然科学学报》2003年第1期25-28,共4页Journal of Natural Science of Hunan Normal University

基　　金：国家自然科学基金资助项目 ( 19810 13)

摘　　要：给定图G =(V ,E) ,设g :V→Z ,f:V→Z和h :E→ [0 ,1]是 3个函数 ,其中Z是整数集 ,如果所有x∈V ,均有g(x) ≤ ∑x∈eh(e) ≤f(x) ,就称Gh =(V ,Eh)是G的一个分数 (g ,f) 因子 ,其中x∈e表示x与e关联 ,Eh =e｜e∈E且h(e)≠ 0 .给出了图有分数 (g ,f) 因子的 2个新的充分条件 .Fractional graph theory is a new research subject in graph theory. Some results concerning fractional matching, fractional coloring etc have been achieved. Given a graph G = (V, E), let f: V&rarrZ, g: V&rarrZ, and h: E&rarr [0, 1] be three functions. We call Gh fractional (g, f)-factor of G if Gh = (V, Eh), where Eh = {e ∈ E1 h(e) ≠ 0}, and g(x &le ∑x∈e h(e) &le f(x) for all x ∈ V(G), where x ∈ e denotes that e is an incident edge with vertex x. In this article, we give two new sufficient conditions for a graph which has a fractional (g, f)-factor.

关 键 词：分数因子 充分条件 度 邻域 分数图论 有限元向图 分数完美匹配 

分 类 号：O157.5[理学—数学]