Binding numbers of fractional k-deleted graphs

Abstract

Let k be an integer with $k \ge 2$. We show that if G be a graph such that $|G| > 4k+1 -4\sqrt {k-1}$ and $bind(G)> {(2k-1)(n-1) \over k(n-2)},$ then G is a fractional k-deleted graph. We also show that in the case where k is even, if G be a graph such that $|G| > 4k+1 -4\sqrt {k}$ and $bind(G)> {(2k-1)(n-1) \over k(n-2)+1},$ then G is a fractional k-deleted graph.