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.
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