An Algorithm Computing the Core of a Konig-Egervary Graph
  A set S of vertices is independent in a graph G if no two vertices from S are adjacent, and alpha(G) is the cardinality of a maximum independent set of G.   G is called a Konig-Egervary graph if its order equals alpha(G)+mu(G), where mu(G) denotes the size of a maximum matching. By core(G) we mean the intersection of all maximum independent sets of G.   To decide whether core(G) is empty is known to be NP-hard.   In this paper, we present some polynomial time algorithms finding core(G) of a Konig-Egervary graph G. 
Vadim E. Levit and Eugen Mandrescu
cs.DM math.CO