Binding number and toughness for matching extension

Abstract A graph G of even order is said to be k -extendable if every matching of size k in G can be extended to a 1-factor of G . Plummer (1988) showed that a graph G is k -extendable if tough ( G ) > k , and we here prove that G is also k -extendable if bind ( G ) > max {k, (7k + 13)/12}.