Maximum Biclique for Star 1,2,3 -free and Bounded Bimodularwidth Twin-free Bipartite Graphs $\star$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911193137938432 |
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| author | de Montgolfier, Fabien Torfs, Renaud |
| author_facet | de Montgolfier, Fabien Torfs, Renaud |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04621 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximum Biclique for Star 1,2,3 -free and Bounded Bimodularwidth Twin-free Bipartite Graphs $\star$ de Montgolfier, Fabien Torfs, Renaud Discrete Mathematics Data Structures and Algorithms 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. |
| title | Maximum Biclique for Star 1,2,3 -free and Bounded Bimodularwidth Twin-free Bipartite Graphs $\star$ |
| topic | Discrete Mathematics Data Structures and Algorithms |
| url | https://arxiv.org/abs/2510.04621 |