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MathNet 2019-part-05 — 184 problems (EN–VI) Question 141

Math Olympiad Vault · MathNet 2019-part-05 — 184 problems (EN–VI)

Question 141

Given any positive real number $\varepsilon$, prove that, for all but finitely many positive integers $v$, any graph on $v$ vertices with at least $(1+\varepsilon) v$ 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.)