唯一可序区间图
Uniquely orderable interval graphs
摘要：
区间图和区间序有着紧密的联系。事实上，区间图的边表示了区间序之间的不可比关系，一般来说，也表示了不同区间序之间的不可比关系。关于给定的区间图与唯一的区间序（直到对偶）相关联的条件的问题自然出现。Fishburn给出了唯一可序的有限连通区间图的一个刻画。我们表明，一个全新的证明，同样的刻画也适用于无限连通区间图。使用逆向数学的工具，我们解释了为什么特征不能从有限到无限的紧凑性，因为它经常发生。
英文摘要：
Interval graphs and interval orders are deeply linked. In fact, edges of an interval graphs represent the incomparability relation of an interval order, and in general, of different interval orders. The question about the conditions under which a given interval graph is associated to a unique interval order (up to duality) arises naturally. Fishburn provided a characterisation for uniquely orderable finite connected interval graphs. We show, by an entirely new proof, that the same characterisation holds also for infinite connected interval graphs. Using tools from reverse mathematics, we explain why the characterisation cannot be lifted from the finite to the infinite by compactness, as it often happens.
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