The number of maximal matchings in polygon rings
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909645191249920 |
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| author | Li, Chengqi Yin, Jinhui Shi, Lingjuan |
| author_facet | Li, Chengqi Yin, Jinhui Shi, Lingjuan |
| contents | A matching of graph $G$ is maximal if it cannot be expanded by adding any edge to create a larger matching. In this paper, for a hexagonal ring $H$ with $n$ hexagons, we show that the number of maximal matchings of $H$ equals to the trace of the product of $n$ matrices, each of which is $S$, $L$, or $R$ according to the type of the connection mode of $H$. Finally, we extend this conclusion to arbitrary polygon rings and provide an algorithm to determine the transition matrices of polygon chains (rings). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08687 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The number of maximal matchings in polygon rings Li, Chengqi Yin, Jinhui Shi, Lingjuan Combinatorics A matching of graph $G$ is maximal if it cannot be expanded by adding any edge to create a larger matching. In this paper, for a hexagonal ring $H$ with $n$ hexagons, we show that the number of maximal matchings of $H$ equals to the trace of the product of $n$ matrices, each of which is $S$, $L$, or $R$ according to the type of the connection mode of $H$. Finally, we extend this conclusion to arbitrary polygon rings and provide an algorithm to determine the transition matrices of polygon chains (rings). |
| title | The number of maximal matchings in polygon rings |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2506.08687 |