On the number of spanning trees in random regular graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2013
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| _version_ | 1866910463078432768 |
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| author | Greenhill, Catherine Kwan, Matthew Wind, David |
| author_facet | Greenhill, Catherine Kwan, Matthew Wind, David |
| contents | Let $d \geq 3$ be a fixed integer. We give an asympotic formula for the expected number of spanning trees in a uniformly random $d$-regular graph with $n$ vertices. (The asymptotics are as $n\to\infty$, restricted to even $n$ if $d$ is odd.) We also obtain the asymptotic distribution of the number of spanning trees in a uniformly random cubic graph, and conjecture that the corresponding result holds for arbitrary (fixed) $d$. Numerical evidence is presented which supports our conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1309_6710 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | On the number of spanning trees in random regular graphs Greenhill, Catherine Kwan, Matthew Wind, David Combinatorics Probability Let $d \geq 3$ be a fixed integer. We give an asympotic formula for the expected number of spanning trees in a uniformly random $d$-regular graph with $n$ vertices. (The asymptotics are as $n\to\infty$, restricted to even $n$ if $d$ is odd.) We also obtain the asymptotic distribution of the number of spanning trees in a uniformly random cubic graph, and conjecture that the corresponding result holds for arbitrary (fixed) $d$. Numerical evidence is presented which supports our conjecture. |
| title | On the number of spanning trees in random regular graphs |
| topic | Combinatorics Probability |
| url | https://arxiv.org/abs/1309.6710 |