English

On Expansion of Random Regular Graphs: Improved Lower Bounds for Small Even Degrees

Combinatorics 2026-04-02 v1

Abstract

We show that a simple scoring-based tie-breaking can help improve lower bounds for the expansion (aka isoperimetric number) of random regular graphs with small even degrees. Specifically, for degrees 4, 6 and 8, we show that, with high probability, the expansions are at least 0.489, 1.120 and 1.813 respectively.

Keywords

Cite

@article{arxiv.2604.00488,
  title  = {On Expansion of Random Regular Graphs: Improved Lower Bounds for Small Even Degrees},
  author = {Pasin Manurangsi},
  journal= {arXiv preprint arXiv:2604.00488},
  year   = {2026}
}