发表机构
New York University; The University of British Columbia（纽约大学; 不列颠哥伦比亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对Kozerenko与Skochko提出的不平衡猜想，通过推导截断和的下界、结合Erdos-Gallai不等式与奇偶性计算完成证明，解决了有限简单图领域的相关猜想问题。
AI 中文摘要
对于有限简单图G的边uv，其不平衡度为|d_G(u)-d_G(v)|，不平衡多重集M_G由G所有边的不平衡度构成。Kozerenko和Skochko猜想，若每条边的不平衡度均为正，则M_G是可图的。我们证明了该猜想。核心方法是：当至少k条边的不平衡度至少为k时，截断和∑_{e∈E(G)}min{k,imb_G(e)}存在下界；该下界可导出边不平衡度非增序列的所有Erdos-Gallai不等式，再经奇偶性计算完成证明。
英文摘要
For an edge $uv$ of a finite simple graph $G$, its imbalance is $|d_G(u)-d_G(v)|$, and the imbalance multiset $M_G$ consists of the imbalances of all edges of $G$. Kozerenko and Skochko conjectured that $M_G$ is graphic whenever every edge has positive imbalance. We prove this conjecture. The main ingredient is the following capacity bound: for every set $A$ of $k$ edges, \[ \sum_{e\in E(G)\setminus A}\min\{k,\operatorname{imb}_G(e)\} \ge k\max\{Δ-k,0\}, \] where $Δ$ is the maximum degree of $G$. This bound yields all Erdős--Gallai inequalities directly; a parity computation completes the proof.
Comments5 pages, no figures; added reference to an earlier independent proof; mathematical content unchanged
