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Found problems: 3

2019 Romanian Masters In Mathematics, 3
Tags: RMM , RMM 2019 , combinatorics , graph theory , cycles , Fedya , probability
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.) [i]Fedor Petrov, Russia[/i]

Kvant 2019, M2557
Tags: RMM , RMM 2019 , combinatorics , graph theory , cycles , Fedya , probability
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.) [i]Fedor Petrov, Russia[/i]

2019 Romanian Master of Mathematics, 3
Tags: RMM , RMM 2019 , combinatorics , graph theory , cycles , Fedya , probability
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.) [i]Fedor Petrov, Russia[/i]