On 1-factors and matching extension

We prove the following: (1) Let G be a graph with a 1-factor and let F be an arbitrary 1-factor of G. If G⧹{a,b} is k-extendable for each ab∈F, then G is k-extendable. (2) Let G be a graph and let M be an arbitrary maximal matching of G. If G⧹{a,b} is k-factor-critical for each ab∈M, then G is k-factor-critical.