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Way to solve max_split enumeration

Hello everyone, I try to solve a problem on graphs. The graphs contain two types of nodes, a first type linked together containing max_cliques that I seek to determine. A second one connected only to the first.

For the moment I enumerate the biggest cliques of the first type, then determines for each the number of nodes of the second type related to this one. Finally I list the one with the largest number of nodes of the second type.   So I'm looking to find the biggest split graph.

Do you have an idea to improve my current way?