{"date_created":"2021-06-22T12:18:59Z","volume":63,"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."}],"scopus_import":"1","_id":"9589","oa":1,"publication_status":"published","publication":"European Journal of Combinatorics","language":[{"iso":"eng"}],"user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","article_processing_charge":"No","publisher":"Elsevier","day":"01","external_id":{"arxiv":["1606.01586"]},"status":"public","author":[{"first_name":"Catherine","last_name":"Greenhill","full_name":"Greenhill, Catherine"},{"full_name":"Isaev, Mikhail","last_name":"Isaev","first_name":"Mikhail"},{"last_name":"Kwan","orcid":"0000-0002-4003-7567","first_name":"Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","full_name":"Kwan, Matthew Alan"},{"first_name":"Brendan D.","last_name":"McKay","full_name":"McKay, Brendan D."}],"oa_version":"Published Version","date_updated":"2023-02-23T14:02:00Z","article_type":"original","doi":"10.1016/j.ejc.2017.02.003","type":"journal_article","page":"6-25","title":"The average number of spanning trees in sparse graphs with given degrees","quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1016/j.ejc.2017.02.003"}],"intvolume":"        63","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>","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.","short":"C. Greenhill, M. Isaev, M.A. Kwan, B.D. McKay, European Journal of Combinatorics 63 (2017) 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>.","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.","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>."},"date_published":"2017-06-01T00:00:00Z","extern":"1","month":"06","year":"2017","publication_identifier":{"issn":["0195-6698"]}}