论文标题
关于增加可计数超图中增加路径的注释
A note on increasing paths in countable hypergraphs
论文作者
论文摘要
Müller和Rödl的旧结果指出，当且仅当正面整数均为$ g $的任何顶点标记时，可计数图$ g $具有一个子图，它的顶点都具有无限的学位，才能找到无限的增加路径。他们询问与边缘标签相似的等效性是否具有肯定的回答。最近，Arman，Elliott和Rödl将这个问题扩展到了线性$ K $均匀的超图$ H $，并概括了顶点标签的原始等价。他们询问Reiterman的边缘标签结果是否可以类似地扩展。我们在$ H $仅承认有限的Berge周期有限的情况下确认了这一点。
An old result of Müller and Rödl states that a countable graph $G$ has a subgraph whose vertices all have infinite degree if and only if for any vertex labeling of $G$ by positive integers, an infinite increasing path can be found. They asked whether an analogous equivalence holds for edge labelings, which Reiterman answered in the affirmative. Recently, Arman, Elliott, and Rödl extended this problem to linear $k$-uniform hypergraphs $H$ and generalized the original equivalence for vertex labelings. They asked whether Reiterman's result for edge labelings can similarly be extended. We confirm this for the case where $H$ admits only finitely many Berge cycles.
