Author

Bo Zhou

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Preprint Sep 2026

Large Complete Minors from a Cheeger Condition

Let $G$ be a graph on $n$ vertices, and let $e_G(S,V(G)\setminus S)$ be the number of edges with exactly one endpoint in $S$. The Cheeger constant and the restricted Cheeger constant of $G$, where $k\ge1$ is real, are, respectively, \[ h(G)=\min_{\substack{\emptyset\ne S\subseteq V(G)\\|S|\le \frac{n}{2}}} \frac{e_G(S,...

Cheng-Li Li, Le Xu, Bo Zhou · 1 citation · ⚡1

Preprint Oct 2026

Positive discrepancy of graphs far from Tur\'an graphs

We prove that, for every $\eps>0$, any $n$-vertex graph that needs at least $\eps n^2$ edge changes to become a Tur\'an graph has positive discrepancy at least $c_\eps n^{5/4}$. Consequently, every such regular graph has second eigenvalue at least $c'_\eps n^{1/4}$. These results prove two conjectures of R\"aty, Sudako...

Le Xu, Bo Zhou · 0 citations