事件结构的好标号问题：一个反例
Nice labeling problem for event structures: a counterexample
摘要：
本文给出了Rozoy和Thiagarajan在1991年提出的一个猜想的反例（也称为“好的标号问题”），该猜想认为任何有限度的（相干的）事件结构都允许有有限个标号，或者等价地说，存在一个函数$f: \mathbb{N} \mapsto \mathbb{N}$，使得度为$\le n$的事件结构最多允许有$f(n)$标号.我们的反例是基于1965年Burling对团数为2且色数任意大的3维盒超图的构造以及Barthélemy和Constantin在1993年建立的事件结构域与中值图之间的双射.
英文摘要：
In this note, we present a counterexample to a conjecture of Rozoy and Thiagarajan from 1991 (called also the nice labeling problem) asserting that any (coherent) event structure with finite degree admits a labeling with a finite number of labels, or equivalently, that there exists a function $f: \mathbb{N} \mapsto \mathbb{N}$ such that an event structure with degree $\le n$ admits a labeling with at most $f(n)$ labels. Our counterexample is based on the Burling's construction from 1965 of 3-dimensional box hypergraphs with clique number 2 and arbitrarily large chromatic numbers and the bijection between domains of event structures and median graphs established by Barthélemy and Constantin in 1993.
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