论文标题
避免道路超越道路
Avoidability beyond paths
论文作者
论文摘要
贝塞格（Beisegel），丘德诺夫斯基（Chudnovsky），古尔维奇（Gurvich），米兰尼（Milanič）和servatius在2019年引入了图表中可避免的路径的概念，这是对可避免的顶点和简单路径的普遍概括。在2020年，Bonamy，Defrain，Hatzel和Thiebaut证明，包含订单$ K $的诱导路径的每个图还包含相同顺序的可避免的诱导路径。他们还询问是否可以将这一结果推广到其他可避免的结构，这使避免能力的概念无法解释。在本文中，我们解决了这个问题：我们指定了配备两个终端顶点的任意图的避免性的概念。我们提供正面和负面的结果，其中一些似乎与Chudnovsky，Norin，Seymour和Turcotte的最新工作有关[Arxiv：2301.13175]。
The concept of avoidable paths in graphs was introduced by Beisegel, Chudnovsky, Gurvich, Milanič, and Servatius in 2019 as a common generalization of avoidable vertices and simplicial paths. In 2020, Bonamy, Defrain, Hatzel, and Thiebaut proved that every graph containing an induced path of order $k$ also contains an avoidable induced path of the same order. They also asked whether one could generalize this result to other avoidable structures, leaving the notion of avoidability up to interpretation. In this paper we address this question: we specify the concept of avoidability for arbitrary graphs equipped with two terminal vertices. We provide both positive and negative results, some of which appear to be related to the recent work by Chudnovsky, Norin, Seymour, and Turcotte [arXiv:2301.13175].
