The Farey graph is uniquely determined by its connectivity

Jan Kurkofka

doi:10.1016/j.jctb.2021.06.006

The Farey graph is uniquely determined by its connectivity

Jan Kurkofka^*

^*Corresponding author for this work

Mathematics

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

Abstract

We show that, up to minor-equivalence, the Farey graph is the unique minor-minimal graph that is infinitely edge-connected but such that every two vertices can be finitely separated.

Original language	English
Pages (from-to)	223-234
Number of pages	12
Journal	Journal of Combinatorial Theory, Series B
Volume	151
Early online date	29 Jun 2021
DOIs	https://doi.org/10.1016/j.jctb.2021.06.006
Publication status	Published - Nov 2021

Keywords

Infinite graph
Farey graph
Characterisation
Connectivity
Infinite edge-connectivity
Infinitely edge-connected graph
Minor
Typical pi-graph

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10.1016/j.jctb.2021.06.006Licence: None: All rights reserved

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title = "The Farey graph is uniquely determined by its connectivity",

abstract = "We show that, up to minor-equivalence, the Farey graph is the unique minor-minimal graph that is infinitely edge-connected but such that every two vertices can be finitely separated.",

keywords = "Infinite graph, Farey graph, Characterisation, Connectivity, Infinite edge-connectivity, Infinitely edge-connected graph, Minor, Typical pi-graph",

author = "Jan Kurkofka",

year = "2021",

month = nov,

doi = "10.1016/j.jctb.2021.06.006",

language = "English",

volume = "151",

pages = "223--234",

journal = "Journal of Combinatorial Theory, Series B",

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AB - We show that, up to minor-equivalence, the Farey graph is the unique minor-minimal graph that is infinitely edge-connected but such that every two vertices can be finitely separated.

KW - Infinite graph

KW - Farey graph

KW - Characterisation

KW - Connectivity

KW - Infinite edge-connectivity

KW - Infinitely edge-connected graph

KW - Minor

KW - Typical pi-graph

U2 - 10.1016/j.jctb.2021.06.006

DO - 10.1016/j.jctb.2021.06.006

M3 - Article

VL - 151

SP - 223

EP - 234

JO - Journal of Combinatorial Theory, Series B

JF - Journal of Combinatorial Theory, Series B

ER -

The Farey graph is uniquely determined by its connectivity

Abstract

Keywords

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