Edge-disjoint cycles with the same vertex set | Research seminar in Discrete Mathematics

Abstract

In 1975, Erdős asked for the maximum number of edges that an n-vertex graph can have if it does not contain two edge-disjoint cycles on the same vertex set. This problem has since been reiterated by several authors including Bollobás in 1978, Pyber, Rödl, and Szemerédi in 1995, and Chen, Erdős, and Staton in 1996. We asymptotically resolve this long-standing problem in a strong form, by showing that, for any given k, the maximum number of edges in an n-vertex graph not containing k edge-disjoint cycles on the same vertex set is n^{1+o(1)}. Joint work with Debsoumya Chakraborti, Abhishek Methuku and Richard Montgomery.

Speaker Intro

Oliver Janzer is a Junior Research Fellow at Trinity College, Cambridge, whose main research interests are Extremal, Probabilistic and Additive Combinatorics. He obtained his PhD in 2020 under the supervision of Timothy Gowers. Between 2020 and 2022 he held an ETH Zurich Postdoctoral Fellowship. In 2022 he won the British Combinatorial Committee’s PhD thesis prize.