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arXiv · 2303.13923

Expansion properties of Whitehead moves on cubic graphs

Laura Grave de Peralta·Alexander Kolpakov
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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.

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Laura Grave de Peralta, Alexander Kolpakov. 2025-10-26. Expansion properties of Whitehead moves on cubic graphs. https://doi.org/10.5802/crmath.691

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