Two more characterizations of König-Egerváry graphs

In this paper, we prove that G is a König-Egerváry graph if and only if for every two maximum independent sets S1,S2 of G, there is a matching from V(G)−S1∪S2 into S1∩S2. Moreover, the same is true, when instead of two sets S1 and S2 we consider an arbitrary König-Egerváry collection.