Maximal independent sets in graphs with given matching number
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909627843608576 |
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| author | Shi, Yongtang Tu, Jianhua Wang, Ziyuan |
| author_facet | Shi, Yongtang Tu, Jianhua Wang, Ziyuan |
| contents | A maximal independent set in a graph $G$ is an independent set that cannot be extended to a larger independent set by adding any vertex from $G$. This paper investigates the problem of determining the maximum number of maximal independent sets in terms of the matching number of a graph. We establish the maximum number of maximal independent sets for general graphs, connected graphs, triangle-free graphs, and connected triangle-free graphs with a given matching number, and characterize the extremal graphs achieving these maxima. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15950 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximal independent sets in graphs with given matching number Shi, Yongtang Tu, Jianhua Wang, Ziyuan Combinatorics 05C69, 05C30, 05C70 A maximal independent set in a graph $G$ is an independent set that cannot be extended to a larger independent set by adding any vertex from $G$. This paper investigates the problem of determining the maximum number of maximal independent sets in terms of the matching number of a graph. We establish the maximum number of maximal independent sets for general graphs, connected graphs, triangle-free graphs, and connected triangle-free graphs with a given matching number, and characterize the extremal graphs achieving these maxima. |
| title | Maximal independent sets in graphs with given matching number |
| topic | Combinatorics 05C69, 05C30, 05C70 |
| url | https://arxiv.org/abs/2412.15950 |