Ubiquity and the Farey graph

Jan Kurkofka

Ubiquity and the Farey graph

Combinatorics 2020-07-01 v2

Authors: Jan Kurkofka

Abstract

We construct a countable planar graph which, for any two vertices $u,v$ and any integer $k\ge 1$ , contains $k$ edge-disjoint order-compatible $u$ -- $v$ paths but not infinitely many. This graph has applications in Ramsey theory, in the study of connectivity and in the characterisation of the Farey graph.

Keywords

graph theory dyck paths bijective combinatorics

Cite

@article{arxiv.1912.02147,
  title  = {Ubiquity and the Farey graph},
  author = {Jan Kurkofka},
  journal= {arXiv preprint arXiv:1912.02147},
  year   = {2020}
}

Comments

8 pages, 5 figures

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