### Abstract

Original language | English |
---|---|

Article number | P1.45 |

Journal | The Electronic Journal of Combinatorics |

Volume | 21 |

Issue number | 1 |

Number of pages | 26 |

ISSN | 1097-1440 |

Publication status | Published - 2014 |

### Keywords

- Spanning trees
- Random regular graphs
- Small subgraph conditioning

### Cite this

*The Electronic Journal of Combinatorics*,

*21*(1), [P1.45].

}

*The Electronic Journal of Combinatorics*, vol. 21, no. 1, P1.45.

**On the number of spanning trees in random regular graphs.** / Greenhill, Catherine; Kwan, Matthew; Wind, David Kofoed.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - On the number of spanning trees in random regular graphs

AU - Greenhill, Catherine

AU - Kwan, Matthew

AU - Wind, David Kofoed

PY - 2014

Y1 - 2014

N2 - Let d >= 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 -> infinity, 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.

AB - Let d >= 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 -> infinity, 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.

KW - Spanning trees

KW - Random regular graphs

KW - Small subgraph conditioning

M3 - Journal article

VL - 21

JO - The Electronic Journal of Combinatorics

JF - The Electronic Journal of Combinatorics

SN - 1097-1440

IS - 1

M1 - P1.45

ER -