Flexible 3-valent graphs of even girth

2025/08/22 by Barbieri, Marco, Zozaya, Andoni
#05C12 #20B25 #20E05 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2508.16289

Abstract

We prove the existence of a connected flexible 3-valent vertex-transitive graph of girth 2ℓ for every integer ℓ. We also give a constructive proof if ℓ is prime.

Citations

• On cubic vertex-transitive graphs of given girth
• On orders of automorphisms of vertex-transitive graphs
• On the number of fixed points of automorphisms of vertex-transitive graphs of bounded valency
• Distinguishing graphs of maximum valence 3
• Cubic vertex-transitive graphs on up to 1280 vertices
• Bounding the order of the vertex-stabiliser in 3-valent\n vertex-transitive and 4-valent arc-transitive graphs

Related

• On vertex-girth-regular graphs: (Non-)existence, bounds and enumeration
• The 4-Regular Edge-Transitive Graphs of Girth 4
• Graphs with large girth and free groups
• Graphs with girth 2ℓ and without longer even holes are 3-colorable
• Bounding the order of the vertex-stabiliser in 3-valent\n vertex-transitive and 4-valent arc-transitive graphs