2025/10/06 by Fabien de Montgolfier, de Montgolfier, Fabien, Renaud Torfs +1
Computer Science · #Advanced Graph Theory Research #Interconnection Networks and Systems #Complexity and Algorithms in Graphs
paper · pdf · doi:10.48550/arxiv.2510.04621
There are three usual definitions of a maximum bipartite clique (biclique) in a bipartite graph : either maximizing the number of vertices, or of edges, or finding a maximum balanced biclique. The first problem can be solved in polynomial time, the last ones are NP-complete. Here we show how these three problems may be efficiently solved for two classes of bipartite graphs: Star123-free twin-free graphs, and bounded bimodularwidth twin-free graphs, a class that may be defined using bimodular decomposition. Our computation requires O(n2) time and requires a decomposition is provided, which takes respectively O(n + m) and O(mn3) time.