Connectivity keeping paths for k-connected bipartite graphs

Luo, Tian and Wu [Discrete Math. 345 (4) (2022) 112788] conjectured that for any tree $T$ with bipartition $(X,Y)$, every $k$-connected bipartite graph $G$ with minimum degree at least $k+w$, where $w=\max \{\mathrm{\mid }X\mathrm{\mid },\mathrm{\mid }Y\mathrm{\mid }\}$, contains a tree $T^{\mathrm{\prime }}\cong T$ such that $\kappa (G-V(T^{\mathrm{\prime }}))\ge k$. In the paper, we confirm the conjecture when $T$ is an odd path on $m$ vertices. We remind that Yang and Tian \cite{YT2} also prove the same result by a different way.