Abstract
A biclique of a graph G is a maximal complete bipartite induced subgraph of G with at least one edge. We define and study the time complexity of the problems of finding the minimum biclique transversal and maximum biclique independent set of a graph G, denoted by αb(G) and τb(G) respectively. We prove that the Biclique-Transversal and Biclique-Independent-Set problems are NP-Complete for the classes of split graphs, planar graphs C4-free with ∆ = 4, and bipartite C4-free graphs with ∆ = 4. In addition, we provide polinomial time algorithms for block graphs and split gem-free graphs. Finally, we introduce the concept of biclique-perfectness.
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