图的分数k-因子

给定图G=(V,E).设a和b是两个非负整数.fE→［0,1］是一个函数.如果     

图的因子和因子分解的若干进展

本文综述了图的的因子和因子分解近年来的一些新结果。主要有图的因子与各种参数之间的关系,图有某种因子的一些充分必要条件,特别是图有ｋ－因子的一些充分条件以及关于图的因子分解和正交因子分解的一些新结果。文中提出了一些新的问题和猜想。     

PROPERTIES OF FRACTIONAL k-FACTORS OF GRAPHS

In this paper the properties of some maximum fractional [0, k]-factors of graphs are presented. And consequently some results on fractional matchings and fractional 1-factors are generalized and a characterization of fractional k-factors is obtained.     

FRACTIONAL (g, f)-FACTORS OF GRAPHS

1 IntroductionThe graphs considered in this paper will be finite undirected graphs wllicll 11lay llavemultiple edges but no loops. Let G be a grapll with vertex set V(G) and edge set E(G). Fora vertex x of G, the degree of x in G is denoted by dG(z). Let g and f be two integer-valuedfunctions defined o11 V(G) such that 0 < g(z) 5 f(x) fOr all x E V(G). Then a (g, f)-factorof G is a spanning 8ubgraph F of G satisfying g(x) < dG(z) 5 f(x) for all x E V(F). Ifg(x) = f(x) for all x E V(…     

图的分数κ-因子

给定图Ｇ＝（Ｖ,Ｅ）．设ａ和ｂ是两个非负整数．是一个函数．如果对所有的均成立,称 ｆ为 Ｇ的一个分数［ａ,ｂ］－ 因子． ａ＝ ｂ＝ κ时,称ｆ为 Ｇ的一个分数 ｋ＝因子．本文给出了一个图有分数 ｋ－因子的充分必要条件．     

图中的最大分数(0,f)-因子

本语文给出了图的一个（０,ｆ）因子是最大因子的特征,并得到了一个图有（ｇ,ｆ）－因子的充分条件,从而了关于分数对集和１－因子的有关结果。     

邻接树图是哈密尔顿图猜想的一个等价命题

本文给出了简单图的邻接树图是哈密尔顿图”猜想的等价命题,阐明只需证明该猜想对2－连通图成立即可,另外,我们给出了该猜想一种特殊情形的构造性证明。     

PROPERTIES OF FRACTIONAL κ-FACTORS OF GRAPHS

In this paper the properties of some maximum fractional [0, κ]-factors of graphs are presented. And consequently some results on fractional matchings and fractional 1-factors are generalized and a characterization of fractional k-factors is obtained.