The immersion-minimal infinitely edge-connected graph

Paul Knappe; Jan Kurkofka

doi:10.48550/arXiv.2207.08459

The immersion-minimal infinitely edge-connected graph

Paul Knappe
, Jan Kurkofka

Mathematics

Research output: Working paper/Preprint › Preprint

28 Downloads (Pure)

Abstract

We show that there is a unique immersion-minimal infinitely edge-connected graph: every such graph contains the halved Farey graph, which is itself infinitely edge-connected, as an immersion minor.

By contrast, any minimal list of infinitely edge-connected graphs represented in all such graphs as topological minors must be uncountable.

Original language	English
Publisher	arXiv
DOIs	https://doi.org/10.48550/arXiv.2207.08459
Publication status	Published - 18 Jul 2022

Access to Document

10.48550/arXiv.2207.08459Licence: Other (please provide link to licence statement

2207.08459v1Other version, 649 KBLicence: Other (please provide link to licence statement

Cite this

@techreport{7d7feb0c306444be83d0359ed1ee17a0,

title = "The immersion-minimal infinitely edge-connected graph",

abstract = " We show that there is a unique immersion-minimal infinitely edge-connected graph: every such graph contains the halved Farey graph, which is itself infinitely edge-connected, as an immersion minor. By contrast, any minimal list of infinitely edge-connected graphs represented in all such graphs as topological minors must be uncountable. ",

author = "Paul Knappe and Jan Kurkofka",

year = "2022",

month = jul,

day = "18",

doi = "10.48550/arXiv.2207.08459",

language = "English",

publisher = "arXiv",

type = "WorkingPaper",

institution = "arXiv",

}

TY - UNPB

T1 - The immersion-minimal infinitely edge-connected graph

AU - Knappe, Paul

AU - Kurkofka, Jan

PY - 2022/7/18

Y1 - 2022/7/18

N2 - We show that there is a unique immersion-minimal infinitely edge-connected graph: every such graph contains the halved Farey graph, which is itself infinitely edge-connected, as an immersion minor. By contrast, any minimal list of infinitely edge-connected graphs represented in all such graphs as topological minors must be uncountable.

AB - We show that there is a unique immersion-minimal infinitely edge-connected graph: every such graph contains the halved Farey graph, which is itself infinitely edge-connected, as an immersion minor. By contrast, any minimal list of infinitely edge-connected graphs represented in all such graphs as topological minors must be uncountable.

U2 - 10.48550/arXiv.2207.08459

DO - 10.48550/arXiv.2207.08459

M3 - Preprint

BT - The immersion-minimal infinitely edge-connected graph

PB - arXiv

ER -

The immersion-minimal infinitely edge-connected graph

Abstract

Access to Document

Fingerprint

Cite this