Connectivity keeping paths for k-connected bipartite graphs

Abstract

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 $w=\max \{|X|,|Y|\}$, contains a tree $T^{\prime }\cong T$ such that $\hat{I}º(G-V(T^{\prime }))\ge k$. 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.

5 pages