An improvement of the previous result on fractional (a,b,k)-critical covered graphs

A graph G is called fractional [a, b]-covered if for every e∈E(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$e\in E(G)$$\end{document}, G has a fractional [a, b]-factor containing e. A graph G is called fractional (a, b, k)-critical covered if after deleting any k vertices of G, the remaining graph of G is fractional [a, b]-covered. In this paper, we pose a Fan-type condition for a graph being fractional (a, b, k)-critical covered, which is an improvement of Zhou, Xu and Sun’s previous result [S. Zhou, Y. Xu, Z. Sun, Degree conditions for fractional (a, b, k)-critical covered graphs, Information Processing Letters 152(2019)105838]. Furthermore, we claim that the main result in this paper is best possible in some sense.