On the generation of bicliques of a graph

This work describes a study on the generation of bicliques of a graph. We show that it is NP-complete to test whether a subset of the vertices of a graph is part of a biclique. We also show that there is no polynomial-time delay algorithm for generating all bicliques in reverse lexicographic order, unless P = NP. On the other hand, we describe different polynomial-time delay algorithms for the generation of bicliques of a graph. We present an algorithm that generates all bicliques of a graph in lexicographic order. We also describe an algorithm that generates all non-induced bicliques of a graph. In addition, we propose specialized efficient algorithms for generating the bicliques of special classes of graphs. Resumo. Este trabalho consiste de um estudo sobre a gerac¸˜ao de bicliques de um grafo. Demonstramos que ´e NP-completo decidir se um subconjunto de v´ertices de um grafo ´e parte de uma biclique. Demonstramos tamb´em que n˜ao existe algoritmo com atraso polinomial para a...

• Type: Journal
• Year: 2007
• Where: DAM
• Authors: Vânia M. F. Dias, Celina M. Herrera de Figueiredo, Jayme Luiz Szwarcfiter
• Keywords: DAM 2007, Lexicographic Order, Polynomial-time Delay Algorithms, Um Grafo