A strengthening of Halin's grid theorem

Jan Kurkofka; Ruben Melcher; Max Pitz

A strengthening of Halin's grid theorem

Combinatorics 2021-04-22 v1

Authors: Jan Kurkofka , Ruben Melcher , Max Pitz

Abstract

We show that for every infinite collection $\mathcal{R}$ 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 $\mathcal{R}$ . This result strengthens Halin's grid theorem by giving control over which specific set of rays is used, while its proof is significantly shorter.

Keywords

graph theory halin's grid theorem infinite rays hexagonal half-grid subdivision

Cite

@article{arxiv.2104.10672,
  title  = {A strengthening of Halin's grid theorem},
  author = {Jan Kurkofka and Ruben Melcher and Max Pitz},
  journal= {arXiv preprint arXiv:2104.10672},
  year   = {2021}
}

Comments

4 pages, 2 figures

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