双偏序的niche图
The niche graphs of doubly partial orders
摘要：
已知双偏序的竞争图是区间图。双偏序的竞争共敌图也被称为区间图，除非它包含一个长度为4的圈作为诱导子图。本文证明了双偏序的小生境图不一定是区间图。事实上，我们证明了，对于每个整数n至少4，存在一个双重偏序，其生态位图包含一个诱导子图同构于一个长度为n的圈。我们还证明了如果双偏序的小生境图是无三角形的，那么它是区间图。
英文摘要：
The competition graph of a doubly partial order is known to be an interval graph. The competition-common enemy graph of a doubly partial order is also known to be an interval graph unless it contains a cycle of length 4 as an induced subgraph. In this paper, we show that the niche graph of a doubly partial order is not necessarily an interval graph. In fact, we prove that, for each integer n at least 4, there exists a doubly partial order whose niche graph contains an induced subgraph isomorphic to a cycle of length n. We also show that if the niche graph of a doubly partial order is triangle-free, then it is an interval graph.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
