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Non-repeated cycle lengths and Sidon sequences

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Abstract

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

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Acknowledgement

The authors would like to thank the referee for their careful reading and many valuable suggestions.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, 230026, China

    Jie Ma & Tianchi Yang

Authors
  1. Jie Ma
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  2. Tianchi Yang
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Correspondence to Jie Ma.

Additional information

This research was supported in part by National Key Research and Development Project SQ2020YFA070080, National Natural Science Foundation of China grants 11622110 and 12125106, and Anhui Initiative in Quantum Information Technologies grant AHY150200.

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Ma, J., Yang, T. Non-repeated cycle lengths and Sidon sequences. Isr. J. Math. 245, 639–674 (2021). https://doi.org/10.1007/s11856-021-2222-1

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  • DOI: https://doi.org/10.1007/s11856-021-2222-1

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