Abstract Graph Factors and Matching Extensions deals with two important branches of graph
theory-factor theory and extendable graphs. Due to the mature techniques and wide ranges …

A graph G is called a fractional (g, f)-covered graph if for any e∈ E (G), G admits a fractional
(g, f)-factor covering e. A graph G is called a fractional (g, f, n)-critical covered graph if for any …

Let G be a graph. Let h: E (G)→[0, 1] be a function. If∑ e∋ xh (e)= k holds for each x∈ V (G),
then we call G [Fh] a fractional k-factor of G with indicator function h where Fh={e∈ E (G): h …

Let G be a graph and a, b and k be nonnegative integers with 1≤a≤b. A graph G is defined
as all fractional (a,b,k)-critical if after deleting any k vertices of G, the remaining graph has all …

Let a, b, k, r be nonnegative integers with 1≤ a≤ b and r≥ 2. Let G be a graph of order n
with n>(a+b)(r(a+b)-2)+aka. In this paper, we first show a characterization for all fractional (a …

In this article, we obtain a sufficient condition related to toughness τ (G) for a graph to be all
fractional (a, b, k)-critical. We prove that if τ (G)≥(b 2− 1)+ aka for some nonnegative …

A graph G is called a fractional [a, b]-covered graph if for each e∈ E (G), G contains a
fractional [a, b]-factor covering e. A graph G is called a fractional (a, b, k)-critical covered …

Let G be a graph, and ka positive integer. Let h: E (G)→[0, 1] be a function. If∑ e∋ xh (e)= k
holds for each x∈ V (G), then we call G [F h] a fractional k-factor of G with indicator function h …

We consider two generalizations of the edge coloring problem in bipartite graphs. The first
problem we consider is the weighted bipartite edge coloring problem where we are given an …

In this paper, we show that every highly edge-connected graph $ G $, under a necessary
and sufficient degree condition, can be edge-decomposed into $ k $ factors $ G_1,\ldots …