Odd-ordered Cayley graphs satisfy Erdős–Gyárfás
Source: github.com/burkh4rt/Cayley-Erdos-Gyarfas-Formalized/tree/11…
Every Cayley graph of a finite group of odd order with an inverse-closed, identity-free generating set of size at least three contains a simple cycle of length 2^n for some n ≥ 2. For a noncyclic group of odd order, two such cycles can be chosen as translates meeting at exactly one vertex. A symmetric figure-eight lifts through an abelian normal subgroup of an odd-order group, and a power-of-two cycle lifts through a normal 2-subgroup of a finite group. The cycle conclusion also holds for finite nilpotent groups with a generating set satisfying the same degree condition.
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