Graph Minors and Metric Spaces

IF 1 2区数学 Q1 MATHEMATICS

Combinatorica Pub Date : 2025-06-13 DOI:10.1007/s00493-025-00150-6

Agelos Georgakopoulos, Panos Papasoglu

引用次数: 0

Abstract

We present problems and results that combine graph-minors and coarse geometry. For example, we ask whether every geodesic metric space (or graph) without a fat H minor is quasi-isometric to a graph with no H minor, for an arbitrary finite graph H. We answer this affirmatively for a few small H. We also present a metric analogue of Menger’s theorem and König’s ray theorem. We conjecture metric analogues of the Erdős–Pósa Theorem and Halin’s grid theorem.

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图次元与度量空间

我们提出了结合图子和粗几何的问题和结果。例如，对于任意有限图H，我们问是否每个没有大H次的测地线度量空间（或图）与没有H次的图是拟等距的。对于一些小H，我们肯定地回答了这个问题。我们还提出了门格尔定理和König射线定理的度量模拟。我们推测了Erdős-Pósa定理和Halin网格定理的度量类似物。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Combinatorica 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： COMBINATORICA publishes research papers in English in a variety of areas of combinatorics and the theory of computing, with particular emphasis on general techniques and unifying principles. Typical but not exclusive topics covered by COMBINATORICA are - Combinatorial structures (graphs, hypergraphs, matroids, designs, permutation groups). - Combinatorial optimization. - Combinatorial aspects of geometry and number theory. - Algorithms in combinatorics and related fields. - Computational complexity theory. - Randomization and explicit construction in combinatorics and algorithms.