Binding number and path-factor critical deleted graphs

Abstract

AbstractA graph G is called a [Formula: see text]-factor deleted graph if G – e has a [Formula: see text]-factor for any [Formula: see text] A graph G is [Formula: see text]-factor critical deleted if for every subset [Formula: see text] with [Formula: see text] the graph [Formula: see text] is [Formula: see text]-factor deleted. Zhou, Bian and Pan [Discrete Appl. Math. (2021) in press] showed that an [Formula: see text]-connected graph G is [Formula: see text]-factor critical deleted if its binding number [Formula: see text] In this paper, we give a new binding number condition for [Formula: see text]-factor critical deleted graphs, which improves the above result.