Intersections and unions of critical independent sets in bipartite graphs

Let G be a simple graph with vertex set V (G), and let Ind(G) denote the family of all independent sets of G. The number d (X) = |X| - |N(X)| is the difference of X ⊆ V (G), and a set A ∈ Ind(G) is critical whenever d(A) = max{d (I): I ∈ Ind(G)} [10]. In this paper we establish various relations between intersections and unions of all critical independent sets of a bipartite graph in terms of its bipartition.