Author

Qing-Hai Liu

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Preprint Sep 2026

Connectivity keeping pendant extensions of paths in $k$-connected graphs and triangle-free graphs

Motivated by Mader's conjecture on connectivity keeping trees, we study trees obtained from paths by adding one pendant vertex, as well as related problems in triangle-free graphs. For an integer $m$ and $1\leq i\leq m-1$, let $P_m^+(i)$ denote the tree obtained from a path of order $m-1$ by adding one pendant vertex a...

Meng-Han Ma, Qing-Hai Liu, Li-Ping Zhang et al. · 0 citations

Preprint Aug 2026

The Bounded-VC chromatic thresholds of graphs

For a graph $H$, the chromatic threshold $\delta_\chi(H)$ is the infimum of $c>0$ such that the chromatic number of every $n$-vertex $H$-free graph with minimum degree at least $cn$ is bounded by a constant depending only on $H$ and $c$. Allen, B\"ottcher, Griffiths, Kohayakawa, and Morris proved that if $\chi(H)=r\geq...

Jin-Ze Hu, Qing-Hai Liu, Li-Ping Zhang et al. · 1 citation