发表机构
Princeton University; Tel Aviv University; University of Waterloo; ETH, Zürich; University of California, San Diego（普林斯顿大学; 特拉维夫大学; 滑铁卢大学; 苏黎世联邦理工学院; 加州大学圣地亚哥分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文将Tutte关于正则图存在度约束生成子图的经典结果推广到超图，证明3-均匀正则超图存在度取三个连续值的子图，并讨论更高均匀性的推广与开放问题。
AI 中文摘要
Tutte的一个经典结果表明，任意$d$-正则图都包含一个生成子图，其中每个顶点的度为$k$或$k+1$，对于每个$1\leq k\leq d$。我们将此结论推广到超图，例如，证明了每个$3$-均匀$d$-正则超图都包含一个子图，其中所有度均为$k, k+1$或$k+2$，对于每个$1\leq k\leq d$。该结论在以下意义下是最优的：仅允许两个连续值的相应结论不成立。我们提供了该结论到更高均匀性的推广，并讨论了若干开放问题。
英文摘要
An old result of Tutte states that any $d$-regular graph contains a spanning subgraph in which every vertex has degree $k$ or $k+1$, for every $1\leq k\leq d$. We generalize this statement to hypergraphs, showing, for example, that every $3$-uniform $d$-regular hypergraph contains a subgraph in which all degrees are $k, k+1$ or $k+2$, for every $1\leq k\leq d$. This statement is best possible in the sense that the corresponding statement with only two allowed consecutive values is not true. We provide generalizations of this statement to higher uniformities and discuss several open problems.
Comments12 pages
