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.

中文翻译：

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关于度数序列优化

我们考虑找到给定图的子图的问题，该子图最大化在其度序列上评估的给定函数。虽然这个问题对于凸函数已经很棘手，但我们表明它可以在多项式时间内解决凸多标准目标。我们接下来考虑可分离目标的问题，当所有顶点函数都是平方时，这已经是 NP-hard 了。我们考虑可分离问题的有色扩展，其中包括臭名昭著的精确匹配问题作为特例，并表明它可以在多项式时间内在任何顶点函数的有界树深度图上解决。我们提到了许多尚待解决的问题中的一些。