Non-repeated cycle lengths and Sidon sequences

Abstract

We prove a conjecture of Boros, Caro, F\"uredi and Yuster on the maximum number of edges in a 2-connected graph without repeated cycle lengths, which is a restricted version of a longstanding problem of Erd\H{o}s. Our proof together with the matched lower bound construction of Boros, Caro, F\"uredi and Yuster show that this problem can be conceptually reduced to the seminal problem of finding the maximum Sidon sequences in number theory.