Seminar series
Date
Tue, 20 Feb 2024
Time
14:00 -
15:00
Location
L4
Speaker
Nemanja Draganić
Organisation
University of Oxford
An $n$-vertex graph $G$ is a $C$-expander if $|N(X)|\geq C|X|$ for every $X\subseteq V(G)$ with $|X|< n/2C$ and there is an edge between every two disjoint sets of at least $n/2C$ vertices.
We show that there is some constant $C>0$ for which every $C$-expander is Hamiltonian. In particular, this implies the well known conjecture of Krivelevich and Sudakov from 2003 on Hamilton cycles in $(n,d,\lambda)$-graphs. This completes a long line of research on the Hamiltonicity of sparse graphs, and has many applications.
Joint work with R. Montgomery, D. Munhá Correia, A. Pokrovskiy and B. Sudakov.