---
_id: '9589'
abstract:
- lang: eng
  text: We give an asymptotic expression for the expected number of spanning trees
    in a random graph with a given degree sequence , provided that the number of edges
    is at least , where  is the maximum degree. A key part of our argument involves
    establishing a concentration result for a certain family of functions over random
    trees with given degrees, using Prüfer codes.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Catherine
  full_name: Greenhill, Catherine
  last_name: Greenhill
- first_name: Mikhail
  full_name: Isaev, Mikhail
  last_name: Isaev
- first_name: Matthew Alan
  full_name: Kwan, Matthew Alan
  id: 5fca0887-a1db-11eb-95d1-ca9d5e0453b3
  last_name: Kwan
  orcid: 0000-0002-4003-7567
- first_name: Brendan D.
  full_name: McKay, Brendan D.
  last_name: McKay
citation:
  ama: Greenhill C, Isaev M, Kwan MA, McKay BD. The average number of spanning trees
    in sparse graphs with given degrees. <i>European Journal of Combinatorics</i>.
    2017;63:6-25. doi:<a href="https://doi.org/10.1016/j.ejc.2017.02.003">10.1016/j.ejc.2017.02.003</a>
  apa: Greenhill, C., Isaev, M., Kwan, M. A., &#38; McKay, B. D. (2017). The average
    number of spanning trees in sparse graphs with given degrees. <i>European Journal
    of Combinatorics</i>. Elsevier. <a href="https://doi.org/10.1016/j.ejc.2017.02.003">https://doi.org/10.1016/j.ejc.2017.02.003</a>
  chicago: Greenhill, Catherine, Mikhail Isaev, Matthew Alan Kwan, and Brendan D.
    McKay. “The Average Number of Spanning Trees in Sparse Graphs with given Degrees.”
    <i>European Journal of Combinatorics</i>. Elsevier, 2017. <a href="https://doi.org/10.1016/j.ejc.2017.02.003">https://doi.org/10.1016/j.ejc.2017.02.003</a>.
  ieee: C. Greenhill, M. Isaev, M. A. Kwan, and B. D. McKay, “The average number of
    spanning trees in sparse graphs with given degrees,” <i>European Journal of Combinatorics</i>,
    vol. 63. Elsevier, pp. 6–25, 2017.
  ista: Greenhill C, Isaev M, Kwan MA, McKay BD. 2017. The average number of spanning
    trees in sparse graphs with given degrees. European Journal of Combinatorics.
    63, 6–25.
  mla: Greenhill, Catherine, et al. “The Average Number of Spanning Trees in Sparse
    Graphs with given Degrees.” <i>European Journal of Combinatorics</i>, vol. 63,
    Elsevier, 2017, pp. 6–25, doi:<a href="https://doi.org/10.1016/j.ejc.2017.02.003">10.1016/j.ejc.2017.02.003</a>.
  short: C. Greenhill, M. Isaev, M.A. Kwan, B.D. McKay, European Journal of Combinatorics
    63 (2017) 6–25.
date_created: 2021-06-22T12:18:59Z
date_published: 2017-06-01T00:00:00Z
date_updated: 2023-02-23T14:02:00Z
day: '01'
doi: 10.1016/j.ejc.2017.02.003
extern: '1'
external_id:
  arxiv:
  - '1606.01586'
intvolume: '        63'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1016/j.ejc.2017.02.003
month: '06'
oa: 1
oa_version: Published Version
page: 6-25
publication: European Journal of Combinatorics
publication_identifier:
  issn:
  - 0195-6698
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: The average number of spanning trees in sparse graphs with given degrees
type: journal_article
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
volume: 63
year: '2017'
...