English

Unavoidable Induced Subgraph of Infinite 2-connected Graphs

Combinatorics 2024-12-06 v2

Abstract

In 1930, Ramsey proved that every infinite graph contains either an infinite clique or an infinite independent set as an induced subgraph. K\"{o}nig proved that every infinite graph contains either a ray or a vertex of infinite degree. In this paper, we establish the 2-connected analog of these results.

Keywords

Cite

@article{arxiv.2211.06416,
  title  = {Unavoidable Induced Subgraph of Infinite 2-connected Graphs},
  author = {Sarah Allred and Guoli Ding and Bogdan Oporowski},
  journal= {arXiv preprint arXiv:2211.06416},
  year   = {2024}
}

Comments

18 pages

R2 v1 2026-06-28T05:42:13.558Z