Abstract

An n-vertex graph G is a C-expander if |N(X)>CX for everyXCV(G) withX<n/2C and there is an edge between every two disjoint sets of at least n/2C' vertices. Weshow that there is some constant C'> 0 for which every C-expander is Hamiltonian. in particularthis implies the well known coniecture of Krivelevich and Sudakov from 2003 on Hamilton cycles in(n, d, `)-graphs. This completes a long line of research on the Hamiltonicity of sparse graphs, andhas many applications. Joint work with R. Montgomery, D. Munh Correia, A. Pokrovskiy and B.Sudakov.

Speaker Intro

Nemanja Dragani' is currently a SNSF postdoctoral fellowship holder at the University of Oxfordworking with Peter Keevash. Previously, he obtained his PhD at ETH Zurich under the supervisionof Benny Sudakov. His primary research interests are in extremal and probabilistic combinatoricsRamsey theory and theoretical computer science.