arXiv:2608.02675 · math.CO · August 2026
A 60-Vertex Lower Bound for Cubic Bipartite Counterexamples to the Erdős-Gyárfás Conjecture
A reproducible computer-assisted result proving that every simple cubic bipartite graph on at most 58 vertices contains a cycle of length 4, 8, or 16. Consequently, any cubic-bipartite counterexample to the Erdős-Gyárfás conjecture has at least 60 vertices. The reproducibility artifact was published on GitHub on July 29, 2026.