Number of Eulerian orientations for Benjamini--Schramm convergent graph sequences
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912047304802304 |
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| author | Bencs, Ferenc Borbényi, Márton Csikvári, Péter |
| author_facet | Bencs, Ferenc Borbényi, Márton Csikvári, Péter |
| contents | For a graph $G$ let $\varepsilon(G)$ denote the number of Eulerian orientations, and $v(G)$ denote the number of vertices of $G$. We show that if $(G_n)_n$ is a sequence of Eulerian graphs that are convergent in Benjamini--Schramm sense, then $\lim\limits_{n\to \infty}\frac{1}{v(G_n)}\ln \varepsilon(G_n)$ is convergent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_18012 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Number of Eulerian orientations for Benjamini--Schramm convergent graph sequences Bencs, Ferenc Borbényi, Márton Csikvári, Péter Combinatorics For a graph $G$ let $\varepsilon(G)$ denote the number of Eulerian orientations, and $v(G)$ denote the number of vertices of $G$. We show that if $(G_n)_n$ is a sequence of Eulerian graphs that are convergent in Benjamini--Schramm sense, then $\lim\limits_{n\to \infty}\frac{1}{v(G_n)}\ln \varepsilon(G_n)$ is convergent. |
| title | Number of Eulerian orientations for Benjamini--Schramm convergent graph sequences |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2409.18012 |