English

Expansion properties of Whitehead moves on cubic graphs

Combinatorics 2025-10-28 v2

Abstract

The present note concerns the "graph of graphs" that has cubic graphs as vertices connected by edges represented by the so-called Whitehead moves. Here, we prove that the outer-conductance of the graph of graphs tends to zero as the number of vertices tends to infinity. This answers a question of K. Rafi in the negative.

Keywords

Cite

@article{arxiv.2303.13923,
  title  = {Expansion properties of Whitehead moves on cubic graphs},
  author = {Laura Grave de Peralta and Alexander Kolpakov},
  journal= {arXiv preprint arXiv:2303.13923},
  year   = {2025}
}

Comments

10 pages, 17 figures