Research on fractional critical covered graphs

A graph $G$ is called a fractional $(g, f)$-covered graph if for any $e \in E(G)$, $G$ admits a fractional $(g, f)$-factor covering $e$. A graph $G$ is called a fractional $(g, f, n)$-critical covered graph if for any $S \subseteq V (G)$ with $|S| = n$, $G-S$ is a fractional $(g, f)$-covered graph. A fractional $(g, f, n)$-critical covered graph is said to be a fractional $(a, b, n)$-critical covered graph if $g(x) = a$ and $f(x) = b$ for every $x \in V (G)$. A fractional $(a, b, n)$-critical covered graph was first defined and studied in [1]. In this article, we investigate fractional $(g, f, n)$-critical covered graphs and present a binding number condition for the existence of fractional $(g, f, n)$-critical covered graphs, which is an improvement and generalization of a previous result obtained in [2].