Author

Meng-Han Ma

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Preprint Oct 2026

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

Motivated by Mader's conjecture on connectivity keeping trees, we study the corresponding problem in triangle-free graphs. For positive integers $k,m$, we first prove that every $k$-connected triangle-free graph $G$ with $\delta(G)\geq k+\left \lceil \frac{m}{2} \right \rceil $ contains a path $P$ of order $m$ such tha...

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

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