Author

Qing-Qing Zeng

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Preprint Aug 2026

Sharp asymptotics for triangle independence and covering numbers

For a graph $G$, let $\alpha_1(G)$ be the maximum size of an edge set containing at most one edge from every triangle, and let $\tau_1(G)$ be the minimum size of an edge set meeting every triangle. Erd\H{o}s, Gallai, and Tuza proved that $\alpha_1(G)+\tau_1(G)=\Omega(m^{2/3})$ for every $m$-edge graph and asked for the...

Zhen Liu, Qing-Qing Zeng · 0 citations

Preprint Sep 2026

Large induced subgraphs with $k$ vertices of maximum degree

We prove that, for every integer $k\ge 2$, there exists a constant $c_k>0$ such that every graph on $n\ge R(k,k)$ vertices with maximum degree $\Delta$ contains an induced subgraph on at least $n-c_k\sqrt{\Delta}$ vertices whose maximum degree is attained by at least $k$ vertices. This confirms a conjecture of Caro and...

Zhen Liu, Qing-Qing Zeng · 0 citations