A forbidden pair for quasi 5-contractible edges
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915441407950848 |
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| author | Kou, Shuai Yang, Weihua Zhang, Mingzu Zhao, Shuang |
| author_facet | Kou, Shuai Yang, Weihua Zhang, Mingzu Zhao, Shuang |
| contents | An edge of a quasi $k$-connected graph is said to be quasi $k$-contractible if the contraction of the edge results in a quasi $k$-connected graph. If every quasi $k$-connected graph without a quasi $k$-contractible edge has either $H_{1}$ or $H_{2}$ as a subgraph, then an unordered pair of graphs $\{H_{1}, H_{2}\}$ is said to be a forbidden pair for quasi $k$-contractible edges. We prove that $\{K_{4}^{-}, \overline{P_{5}}\}$ is a forbidden pair for quasi 5-contractible edges, where $K_{4}^{-}$ is the graph obtained from $K_{4}$ by removing just one edge and $\overline{P_{5}}$ is the complement of a path on five vertices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08563 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A forbidden pair for quasi 5-contractible edges Kou, Shuai Yang, Weihua Zhang, Mingzu Zhao, Shuang Combinatorics 05C40 An edge of a quasi $k$-connected graph is said to be quasi $k$-contractible if the contraction of the edge results in a quasi $k$-connected graph. If every quasi $k$-connected graph without a quasi $k$-contractible edge has either $H_{1}$ or $H_{2}$ as a subgraph, then an unordered pair of graphs $\{H_{1}, H_{2}\}$ is said to be a forbidden pair for quasi $k$-contractible edges. We prove that $\{K_{4}^{-}, \overline{P_{5}}\}$ is a forbidden pair for quasi 5-contractible edges, where $K_{4}^{-}$ is the graph obtained from $K_{4}$ by removing just one edge and $\overline{P_{5}}$ is the complement of a path on five vertices. |
| title | A forbidden pair for quasi 5-contractible edges |
| topic | Combinatorics 05C40 |
| url | https://arxiv.org/abs/2508.08563 |