Exact Exponential-Time Algorithms for Finding Bicliques in a Graph

Throughout the paper all graphs G = (V,E) are undirected and simple. An induced biclique of G is a complete bipartite induced subgraph of G. A noninduced biclique is a complete bipartite (not necessarily induced) subgraph of G. Equivalently, the pair (X, Y ) of disjoint vertex subsets X ⊆ V and Y ⊆ V is a non-induced biclique of G if {x, y} ∈ E for all x ∈ X and y ∈ Y . If, additionally, X and Y are independent sets, then (X, Y ) is also an induced biclique of G. Let the pair (X, Y ) be an induced or non-induced biclique. We call it a (k1, k2) biclique if |X| = k1 and |Y | = k2. Its cardinality is |X|+ |Y |.