Quadratic Degree Sequence Optimization and the Critical Roots of a Graph

Frédéric Meunier; Shmuel Onn

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arXiv · 2608.05827

Quadratic Degree Sequence Optimization and the Critical Roots of a Graph

Frédéric Meunier·Shmuel Onn

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Abstract

The degree sequence optimization problem is to find a subgraph of a given graph which maximizes the sum over all vertices of a given function evaluated at the subgraph degree of that vertex. Here we study this problem and its complexity for quadratic functions. In particular, we introduce the critical roots of a graph, and show they define intervals over which the optimal value of the problem, as the quadratic root varies, is convex piecewise affine.

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Frédéric Meunier, Shmuel Onn. 2026-08-06. Quadratic Degree Sequence Optimization and the Critical Roots of a Graph. https://arxiv.org/abs/2608.05827

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