Connectivity keeping paths for k-connected bipartite graphs

Abstract

Luo, Tian and Wu [Discrete Math. 345(4) (2022) 112788] conjectured that for any tree [Formula: see text] with bipartition [Formula: see text], every [Formula: see text]-connected bipartite graph [Formula: see text] with minimum degree at least [Formula: see text], where [Formula: see text], contains a tree [Formula: see text] such that [Formula: see text]. In the paper, we confirm the conjecture when [Formula: see text] is an odd path on [Formula: see text] vertices. We remind that Yang and Tian [Proof of a conjecture on connectivity keeping odd paths in k-connected bipartite graphs, arXiv:2209.08373v2] also prove the same result by a different way.