On Degree Sequence Optimization

03/11/2020

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by   Shmuel Onn, et al.

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We consider the problem of finding a subgraph of a given graph which maximizes a given function evaluated at its degree sequence. While the problem is intractable already for convex functions, we show that it can be solved in polynomial time for convex multi-criteria objectives. We next consider the problem with separable objectives, which is NP-hard already when all vertex functions are the square. We consider a colored extension of the separable problem, which includes the notorious exact matching problem as a special case, and show that it can be solved in polynomial time on graphs of bounded tree-depth for any vertex functions. We mention some of the many remaining open problems.