Non-repeated cycle lengths and Sidon sequences

We prove a conjecture of Boros, Caro, Furedi 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 Erdos. Our proof together with the matched lower bound construction of Boros, Caro, Fuuredi and Yuster show that this problem can be conceptually reduced to the seminal problem of finding the maximum Sidon sequences in number theory.

Automated summary

The research proves that the maximum number of edges in a 2-connected graph without repeated cycle lengths can be conceptually reduced to the classic problem of finding the maximum Sidon sequences in number theory, as shown by the proof and the lower bound construction.