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