Binding number conditions for $(a,b,k)$-critical graphs

Bull. Korean Math. Soc. 2008 Vol. 45, No. 1, 53-57 Published online March 1, 2008

Sizhong Zhou Jiangsu University of Science and Technology

Abstract : 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.