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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.12459 |
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| _version_ | 1866909306606059520 |
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| author | de Panafieu, Élie |
| author_facet | de Panafieu, Élie |
| contents | We derive the asymptotic expansion (asymptotics with an arbitrary number of error terms) of k-regular graphs by applying the Laplace method on a recent exact formula from Caizergues and de Panafieu (2023). We also deduce the asymptotic expansion of connected k-regular graphs using standard techniques for divergent series developed by Wright (1970) and Bender (1975), and quantify its closeness to the asymptotic expansion of k-regular graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12459 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic expansion of regular and connected regular graphs de Panafieu, Élie Combinatorics We derive the asymptotic expansion (asymptotics with an arbitrary number of error terms) of k-regular graphs by applying the Laplace method on a recent exact formula from Caizergues and de Panafieu (2023). We also deduce the asymptotic expansion of connected k-regular graphs using standard techniques for divergent series developed by Wright (1970) and Bender (1975), and quantify its closeness to the asymptotic expansion of k-regular graphs. |
| title | Asymptotic expansion of regular and connected regular graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2408.12459 |