Connectivity keeping paths for k-connected bipartite graphs
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909437133848576 |
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| author | Ji, Meng |
| author_facet | Ji, Meng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08405 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Connectivity keeping paths for k-connected bipartite graphs Ji, Meng Combinatorics 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. |
| title | Connectivity keeping paths for k-connected bipartite graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2312.08405 |