--- _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 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. European Journal of Combinatorics. 2017;63:6-25. doi:10.1016/j.ejc.2017.02.003 apa: Greenhill, C., Isaev, M., Kwan, M. A., & McKay, B. D. (2017). The average number of spanning trees in sparse graphs with given degrees. European Journal of Combinatorics. Elsevier. https://doi.org/10.1016/j.ejc.2017.02.003 chicago: Greenhill, Catherine, Mikhail Isaev, Matthew Alan Kwan, and Brendan D. McKay. “The Average Number of Spanning Trees in Sparse Graphs with given Degrees.” European Journal of Combinatorics. Elsevier, 2017. https://doi.org/10.1016/j.ejc.2017.02.003. ieee: C. Greenhill, M. Isaev, M. A. Kwan, and B. D. McKay, “The average number of spanning trees in sparse graphs with given degrees,” European Journal of Combinatorics, 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.” European Journal of Combinatorics, vol. 63, Elsevier, 2017, pp. 6–25, doi:10.1016/j.ejc.2017.02.003. 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' ...