Binding number and path-factor critical deleted graphs
Yuan Chen, Guowei Dai · AKCE International Journal of Graphs and Combinatorics · 2022
A graph G is called a P≥k-factor deleted graph if G – e has a P≥k-factor for any e∈E(G). A graph G is (P≥k,n)-factor critical deleted if for every subset V′⊆V(G) with |V′|=n, the graph G−V′ is P≥k-factor deleted. Zhou, Bian and Pan [Discrete Appl. Math. (2021) in press] showed that an (n+2)-connected graph G is (P≥3,n)-factor critical deleted if its binding number bind(G)>n+32. In this paper, we give a new binding number condition for (P≥3,n)-factor critical deleted graphs, which improves the above result.