{"id":"palomar/PALOMAR-2026-11-04-000015","url":"https://github.com/burkh4rt/Cayley-Erdos-Gyarfas-Formalized/tree/111aa033acfab934208ce6b2e0cebecacfd6bd24","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-11-04-000015-v1.json","repo":"https://github.com/burkh4rt/Cayley-Erdos-Gyarfas-Formalized","tags":["math.CO","math.GR","msc:05C38","msc:05C25"],"score":0,"title":"Odd-ordered Cayley graphs satisfy Erdős–Gyárfás","trust":"high","domain":"math.CO","source":"palomar","authors":["Michael C. Burkhart"],"reviews":0,"subject":"math.CO","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-11-04","reactions":{},"formalized":true,"formalizes":[{"title":"Odd-ordered Cayley graphs satisfy Erdős–Gyárfás","identifier":"arXiv:2611.05060v1","relationship":"formalizes"}]}