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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2509.25809 |
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| _version_ | 1866909816493965312 |
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| author | Kou, Shuai Qin, Chengfu Yang, Weihua Zhang, Mingzu Zhao, Shuang |
| author_facet | Kou, Shuai Qin, Chengfu 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. We show that every 5-connected graph contains a quasi 5-contractible edge. Furthermore, we prove that a quasi 5-connected graph possesses a quasi 5-contractible edge, if the degree sum of any two vertices with distance at most two is at least 9. This result strengthens a theorem proved by Kriesell when $k=4$ (M. Kriesell, A degree sum condition for the existence of a contractible edge in a $k$-connected graph, J. Combin. Theory Ser. B 82(2001)81-101). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25809 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A degree sum condition for the existence of a quasi 5-contractible edge in a quasi 5-connected graph Kou, Shuai Qin, Chengfu 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. We show that every 5-connected graph contains a quasi 5-contractible edge. Furthermore, we prove that a quasi 5-connected graph possesses a quasi 5-contractible edge, if the degree sum of any two vertices with distance at most two is at least 9. This result strengthens a theorem proved by Kriesell when $k=4$ (M. Kriesell, A degree sum condition for the existence of a contractible edge in a $k$-connected graph, J. Combin. Theory Ser. B 82(2001)81-101). |
| title | A degree sum condition for the existence of a quasi 5-contractible edge in a quasi 5-connected graph |
| topic | Combinatorics 05C40 |
| url | https://arxiv.org/abs/2509.25809 |