Given any positive real number ε, prove that, for all but finitely many positive integers v, any graph on v vertices with at least (1+ε)v edges has two distinct simple cycles of equal lengths.
(Recall that the notion of a simple cycle does not allow repetition of vertices in a cycle.)Fedor Petrov, Russia RMMRMM 2019combinatoricsgraph theorycyclesFedyaprobability