Graphs with given automorphism group and large clique number

TL;DR

This paper proves that for any finite automorphism group, there exist graphs with arbitrarily large clique numbers, strengthening previous results about their genus.

Contribution

The authors provide a concise proof that graphs realizing any finite automorphism group can have unbounded clique number, advancing understanding of graph symmetry and structure.

Findings

Graphs with any finite automorphism group can have arbitrarily large clique numbers

Unbounded clique number implies complex local structure in such graphs

Strengthens previous results about graph genus with respect to automorphism groups

Abstract

Barbieri recently showed that the finite graphs realising any given finite automorphism group have unbounded genus, answering a question of Cornwell et al. In this note we give a short proof of a stronger result: they have unbounded clique number.