In this paper, we prove that every graph with average degree at least $s+t+2$ has a vertex partition into two parts, such that one part has average degree at least s, and the other part has average degree at least t. This solves a conjecture of Csóka, Lo, Norin, Wu and Yepremyan.

中文翻译：

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平均度约束下的图划分

在本文中，我们证明每个具有平均度的图至少$s+t+2$顶点划分为两部分，其中一部分的平均度数至少为s，另一部分的平均度数至少为t。这解决了 Csóka、Lo、Norin、Wu 和 Yepremyan 的猜想。