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arXiv · 2312.08405

Connectivity keeping paths for k-connected bipartite graphs

Meng Ji
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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 $T'\cong T$ such that $κ(G-V(T'))\geq k$. 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.

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Meng Ji. 2024-12-22. Connectivity keeping paths for k-connected bipartite graphs. https://arxiv.org/abs/2312.08405

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