置换诱导的竞争图
Competition graphs induced by permutations
摘要：
在以前的工作中，Cho和Kim研究了由双偏序产生的竞争图。在这篇文章中，我们考虑一个相关的问题，竞争图，而不是诱导置换。我们首先表明，这种方法产生了相同的类的竞争图的双重偏序。此外，我们观察到，$123$和$132$模式的置换诱导相关的竞争图中的边缘。我们分类的竞争图所产生的$132$ -避免置换，并表明，这些图必须避免长度为3的诱导路径图。最后，我们考虑了置换的加权竞争图，并给出了在该情况下的一些初步的计数和结构结果。
英文摘要：
In prior work, Cho and Kim studied competition graphs arising from doubly partial orders. In this article, we consider a related problem where competition graphs are instead induced by permutations. We first show that this approach produces the same class of competition graphs as the doubly partial order. In addition, we observe that the $123$ and $132$ patterns in a permutation induce the edges in the associated competition graph. We classify the competition graphs arising from $132$-avoiding permutations and show that those graphs must avoid an induced path graph of length 3. Finally, we consider the weighted competition graph of permutations and give some initial enumerative and structural results in that setting.
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