基于结构参数的树子图包含问题的二分法
Dichotomies for Tree Minor Containment with Structural Parameters
AI总结：
针对树子图包含问题，本文依据直径、路径宽度和路径离心率三个结构参数给出计算复杂性二分法，刻画其可处理与难处理边界。
摘要：
判断一个图$G$是否包含另一个图$H$作为子图（minor）的问题被称为子图包含问题（minor containment problem），是图算法领域的一个基本问题。虽然当$G$和$H$为一般图时该问题是NP完全的，但在更受限的图类上有时是可处理的。本研究聚焦于$G$和$H$均为树的情形，即树子图包含问题（tree minor containment problem）。即使在这种情况下，该问题已知仍是NP完全的。相比之下，当两棵树均为毛虫图（caterpillars），或$H$的最大度为常数时，已有多项式时间算法。我们的研究旨在阐明树子图包含问题可处理性与不可处理性之间的边界。具体而言，我们基于三个结构参数给出了该问题计算复杂性的二分法：直径（diameter）、路径宽度（pathwidth）和路径离心率（path eccentricity）。
英文摘要：
The problem of determining whether a graph $G$ contains another graph $H$ as a minor, referred to as the minor containment problem, is a fundamental problem in the field of graph algorithms. While it is NP-complete when $G$ and $H$ are general graphs, it is sometimes tractable on more restricted graph classes. This study focuses on the case where both $G$ and $H$ are trees, known as the tree minor containment problem. Even in this case, the problem is known to be NP-complete. In contrast, polynomial-time algorithms are known for the case when both trees are caterpillars or when the maximum degree of $H$ is a constant. Our research aims to clarify the boundary of tractability and intractability for the tree minor containment problem. Specifically, we provide dichotomies for the computational complexities of the problem based on three structural parameters: the diameter, pathwidth, and path eccentricity.
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。
