Comptes Rendus
Research article - Combinatorics, Geometry and Topology
Expansion properties of Whitehead moves on cubic graphs
Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1825-1836.

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.

Cette note porte sur le « graphe des graphes », dont les sommets sont des graphes trivalents reliés par des arêtes correspondant aux transformations de Whitehead. Nous montrons ici que la conductance externe de ce graphe tend vers zéro lorsque le nombre de sommets tend vers l’infini. Cela donne une réponse négative à la question posée par K. Rafi.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/crmath.691
Classification: 05C48, 05C75, 05C90
Keywords: Trivalent graph, cubic graph, expander graph, Whitehead move, conductance
Mots-clés : Graphes trivalents, graphes expanseurs, transformation de Whitehead, conductance

Laura Grave de Peralta 1; Alexander Kolpakov 2

1 Impact Initiatives, 9 Chemin de Balexert, 1219 Geneva, Switzerland
2 University of Austin, 522 Congress Ave., Austin, TX 78701, United States
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     title = {Expansion properties of {Whitehead} moves on cubic graphs},
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Laura Grave de Peralta; Alexander Kolpakov. Expansion properties of Whitehead moves on cubic graphs. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1825-1836. doi : 10.5802/crmath.691. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.691/

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