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Research seminar in Discrete Mathematics
Hamiltonicity of expanders: optimal bounds and applications
Hamiltonicity of expanders: optimal bounds and applications
Organizer
Benjamin Sudakov
Speaker
Nemanja Draganić
Time
Tuesday, May 21, 2024 5:05 PM - 6:15 PM
Venue
Online
Online
Zoom 787 662 9899
(BIMSA)
Abstract
An $n$-vertex graph $G$ is a $C$-expander if $|N(X)| \ge C|X|$ for every $X \subseteq V(G)$ with $|X| \lt n/2C$ 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.