Ubiquity and the Farey graph

Jan Kurkofka

doi:10.1016/j.ejc.2021.103326

Ubiquity and the Farey graph

Jan Kurkofka^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We construct a countable planar graph which, for any two vertices u, v and any integer k ≥ 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.

Original language	English
Article number	103326
Number of pages	8
Journal	European Journal of Combinatorics
Volume	95
Early online date	19 Mar 2021
DOIs	https://doi.org/10.1016/j.ejc.2021.103326
Publication status	Published - Jun 2021

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title = "Ubiquity and the Farey graph",

abstract = "We construct a countable planar graph which, for any two vertices u, v and any integer k ≥ 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. ",

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AB - We construct a countable planar graph which, for any two vertices u, v and any integer k ≥ 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.

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JF - European Journal of Combinatorics

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Ubiquity and the Farey graph

Abstract

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