Bulletin of the
Korean Mathematical Society BKMS

Let $G$ be a graph, and let $a,b,k$ be integers with $0\leq a\leq b,k\geq 0$. Then graph $G$ is called an $(a,b,k)$-critical graph if after deleting any $k$ vertices of $G$ the remaining graph of $G$ has an $[a,b]$-factor. In this paper, the relationship between binding number bind$(G)$ and $(a,b,k)$-critical graph is discussed, and a binding number condition for a graph to be $(a,b,k)$-critical is given.

Keywords: graph, $[a,b]$-factor, binding number, $(a,b,k)$-critical graph

MSC numbers: 05C70