Author

Cai-Hong Yang

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Preprint Sep 2026

A sharp density bound for 5-connected graphs with no $\Ke$ minor

Let $\Ke$ be obtained from $K_7$ by deleting two independent edges. We prove that every 5-connected graph on $n\ge7$ vertices with at least $4n-9$ edges contains a $\Ke$ minor, settling Conjecture~1.4 of Dvo\v r\'ak, Norin and Rahman (arXiv preprint 2609.17760v1). The bound is sharp. We prove the stronger statement tha...

Caibing Chang, Zi-Jian Deng, Qin-Fei Tang et al. · 0 citations

Preprint Jul 2026

The Tur\'an number of the Cartesian product of trees via star-flip

Motivated by Erd\H{o}s's conjecture on the Tur\'an number of degenerate bipartite graphs, Brada\v{c}, Janzer, Sudakov and Tomon proved that $ \ex(n,T \Box P)=\Theta_{T,P}(n^{3/2})$ for every nontrivial tree $T$ and every nontrivial path $P$, and conjectured that the same order of magnitude holds for the Cartesian produ...

Lan Wang, Cai-Hong Yang · 0 citations