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arXiv · 2402.06603

Hamiltonicity of expanders: optimal bounds and applications

Nemanja Draganić·Richard Montgomery·David Munhá Correia·Alexey Pokrovskiy·Benny Sudakov
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Abstract

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 $(n,d,λ)$-graphs. This completes a long line of research on the Hamiltonicity of sparse graphs, and has many applications, including to the Hamiltonicity of random Cayley graphs.

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Nemanja Draganić, Richard Montgomery, David Munhá Correia, Alexey Pokrovskiy, Benny Sudakov. 2024-04-14. Hamiltonicity of expanders: optimal bounds and applications. https://arxiv.org/abs/2402.06603

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