{"ID":2859775,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.04621","arxiv_id":"2510.04621","title":"Maximum Biclique for Star 1,2,3 -free and Bounded Bimodularwidth Twin-free Bipartite Graphs $\\star$","abstract":"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(n^2) time and requires a decomposition is provided, which takes respectively O(n + m) and O(mn^3) time.","short_abstract":"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 b...","url_abs":"https://arxiv.org/abs/2510.04621","url_pdf":"https://arxiv.org/pdf/2510.04621v1","authors":"[\"Fabien de Montgolfier\",\"Renaud Torfs\"]","published":"2025-10-06T09:32:05Z","proceeding":"cs.DM","tasks":"[\"cs.DM\",\"cs.DS\"]","methods":"[]","has_code":false}