The degree sequence optimization problem is to find a subgraph of a given graph which maximizes the sum of given functions evaluated at the subgraph degrees. Here we study this problem by replacing degree sequences, via suitable nonlinear transformations, by suitable degree enumerators, and we introduce suitable degree enumerator polytopes. We characterize their vertices, that is, the extremal degree enumerators, for complete graphs and some complete bipartite graphs, and use these characterizations to obtain simpler and faster algorithms for optimization over degree sequences for such graphs.

翻译：度序列优化问题旨在寻找给定图的子图，使得该子图顶点度数的给定函数之和最大化。本文通过合适的非线性变换，将度序列替换为相应的度枚举元，并引入相应的度枚举元多面体来研究该问题。我们刻画了这些多面体的顶点（即极态度枚举元）在完全图及某些完全二分图上的结构，并利用这些刻画结果，为此类图上的度序列优化问题设计了更简洁、更快速的算法。