English

The immersion-minimal infinitely edge-connected graph

Combinatorics 2024-03-01 v2

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.

Keywords

Cite

@article{arxiv.2207.08459,
  title  = {The immersion-minimal infinitely edge-connected graph},
  author = {Paul Knappe and Jan Kurkofka},
  journal= {arXiv preprint arXiv:2207.08459},
  year   = {2024}
}

Comments

19 pages, 4 figures, to appear in JCTB, tikz code of figures in comments

R2 v1 2026-06-25T00:59:58.496Z