Asymptotic number of edge-colored regular graphs
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911401680830464 |
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| author | Borinsky, Michael Meroni, Chiara Wiesmann, Maximilian |
| author_facet | Borinsky, Michael Meroni, Chiara Wiesmann, Maximilian |
| contents | We prove a formula for the asymptotic number of edge-colored regular graphs with a prescribed set of allowed vertex-incidence structures. The formula depends on specific critical points of a polynomial encoding the vertex-incidences. As an application, we compute the expected number of proper $c$-edge-colorings of a large random $k$-regular graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18994 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotic number of edge-colored regular graphs Borinsky, Michael Meroni, Chiara Wiesmann, Maximilian Combinatorics 05C30, 41A60 (Primary) 05A15, 05C15 (Secondary) We prove a formula for the asymptotic number of edge-colored regular graphs with a prescribed set of allowed vertex-incidence structures. The formula depends on specific critical points of a polynomial encoding the vertex-incidences. As an application, we compute the expected number of proper $c$-edge-colorings of a large random $k$-regular graph. |
| title | Asymptotic number of edge-colored regular graphs |
| topic | Combinatorics 05C30, 41A60 (Primary) 05A15, 05C15 (Secondary) |
| url | https://arxiv.org/abs/2601.18994 |