English

Long induced paths in expanders

Combinatorics 2025-03-05 v2

Abstract

We prove that any bounded degree regular graph with sufficiently strong spectral expansion contains an induced path of linear length. This is the first such result for expanders, strengthening an analogous result in the random setting by Dragani\'c, Glock and Krivelevich. More generally, we find long induced paths in sparse graphs that satisfy a mild upper-uniformity edge-distribution condition.

Keywords

Cite

@article{arxiv.2402.02256,
  title  = {Long induced paths in expanders},
  author = {Nemanja Draganić and Peter Keevash},
  journal= {arXiv preprint arXiv:2402.02256},
  year   = {2025}
}

Comments

7 pages

R2 v1 2026-06-28T14:37:23.062Z