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.

翻译：在二部图中，最大二部团（双团）通常有三种定义方式：最大化顶点数、最大化边数，或寻找最大平衡双团。第一个问题可在多项式时间内求解，后两者则属于NP完全问题。本文展示了如何针对两类二部图高效求解这三个问题：星1,2,3-自由无孪生图，以及有界双模宽无孪生图（后者可通过双模分解定义）。我们的计算复杂度为O(n^2)，但需预先获得分解结构，其构建时间分别为O(n + m)和O(mn^3)。