A strengthening of Halin's grid theorem

Jan Kurkofka; Ruben Melcher; Max Pitz

doi:10.1112/mtk.12135

A strengthening of Halin's grid theorem

Jan Kurkofka, Ruben Melcher^*, Max Pitz

^*Corresponding author for this work

Mathematics

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Abstract

We show that for every infinite collection ℛ of disjoint equivalent rays in a graph G there is a subdivision of the hexagonal half-grid in G such that all its vertical rays belong to ℛ. This result strengthens Halin's grid theorem by giving control over which specific set of rays is used, while its proof is significantly shorter.

Original language	English
Pages (from-to)	1009-1013
Number of pages	5
Journal	Mathematika
Volume	68
Issue number	4
Early online date	15 Jul 2022
DOIs	https://doi.org/10.1112/mtk.12135
Publication status	Published - Oct 2022

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AB - We show that for every infinite collection ℛ of disjoint equivalent rays in a graph G there is a subdivision of the hexagonal half-grid in G such that all its vertical rays belong to ℛ. This result strengthens Halin's grid theorem by giving control over which specific set of rays is used, while its proof is significantly shorter.

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DO - 10.1112/mtk.12135

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A strengthening of Halin's grid theorem

Abstract

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