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From a bipartite graph I wish to find the largest complete bipartite subgraph. From what I've been able to gather, finding complete subgraphs seem to be an NP problem.

I'm completely lost as to how to approach this problem. Should I consider a brute force approach?

If the above isn't possible, is it possible to merely determine the number of components in the maximum complete bipartite? Given two sets M={A,B,C,D,E} and N={a,b,c} and given the connections, would it be possible to arrive to a conclusion that, for example, there are 3 M nodes and 2 N nodes in the largest complete subgraph?

Mercury
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    Run a Bron--Kerbosch variant: https://www.computer.org/csdl/proceedings/hicss/2008/3075/00/30750472.pdf – David Eisenstat Aug 15 '18 at 16:28
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    From @DavidEisenstat 's answer, there is a difference between looking for the one with the largest number of vertices and the largest number of edges. There is a polynomial time algorithm for the largest number of vertices. The largest number of edges is NP-complete. – btilly Aug 15 '18 at 17:01

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