关于分数(g,f)-2-覆盖图

设G是一个图,并设h是定义在图G的边集E(G)上的一个函数,使对任意的e∈E(G),有h(e)∈0,1]。令dhG(x)= x瘕?h(e),则称dhG(x)是G中顶点x的分数度。若h满足对任意的x∈V(G),有g(x)≤dhG(x)≤f(x),则称h是G的一个分数(g,f)-因子。一个图称为分数(g,f)-2-覆盖图,如果对图G中的任何两条边e1和e2,G都有一个分数(g,f)-因子h满足h(e1)=1和h(e2)。本文给出了一个图是分数(g,f) 2 覆盖图的充分必要条件。

On fractional (g,f)-2-covered graphs

Let G be a graph, a fractional (g,f) -factor is a function h that assigns to each edge of a graph G a number in 0,1]so that for each vertex x we have g(x)≤d~h_G(x)≤f(x), where d~h _G(x)=_(x∈e)h(e)(the sum is taken over all edges incident to x) is a fractional degree of x in G. A graph G is fractional (g,f)-2-covered if for any two edges e_1 and e_2 of G there is a fractional (g,f) -factor h such that h(e_1)=1 and h(e_2)=1. In this paper, a necessary and sufficient condition for a graph to be fractional (g,f) -2-covered is given.