小半径部分上路径分解的结构对偶性
组合数学
2025-07-23 v2
摘要
一个容易观察到的结论是:若图 容许其各部分具有小半径的路径分解,则 不包含 或 的大细分作为(拟)测地子图。我们表明这些事实上是此类小径向宽度路径分解的唯一障碍,并证明了以圈与细分星代替路径作为模型的分解的类似结果。借助我们的结果,我们以强形式确认了 Georgakopoulos 与 Papasoglu 关于分别与路径、圈和细分星拟等距的图的脂肪次要刻画的猜想。为此,我们通过有界径向宽度与伸展的图分解给出了图间拟等距的一种新视角。这一新视角使我们能够证明粗图论中的进一步结果,因此可能具有独立意义。
引用
@article{arxiv.2307.08497,
title = {A structural duality for path-decompositions into parts of small radius},
author = {Sandra Albrechtsen and Reinhard Diestel and Ann-Kathrin Elm and Eva Fluck and Raphael W. Jacobs and Paul Knappe and Paul Wollan},
journal= {arXiv preprint arXiv:2307.08497},
year = {2025}
}
备注
This new version has a completely rewritten Introduction, which takes into account several developments occurring close or parallel to the first publication; after the Introduction, we made only restructurings, and added a few propositions and some small corrections and amendments