{"intvolume":"        21","language":[{"iso":"eng"}],"issue":"1","oa_version":"Published Version","main_file_link":[{"url":"https://doi.org/10.37236/3752","open_access":"1"}],"title":"On the number of spanning trees in random regular graphs","quality_controlled":"1","scopus_import":"1","date_published":"2014-02-28T00:00:00Z","article_type":"original","publisher":"The Electronic Journal of Combinatorics","year":"2014","day":"28","publication_identifier":{"eissn":["1077-8926"]},"volume":21,"date_updated":"2023-02-23T14:02:12Z","type":"journal_article","extern":"1","publication_status":"published","publication":"The Electronic Journal of Combinatorics","abstract":[{"text":"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→∞, 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.","lang":"eng"}],"article_number":"P1.45","doi":"10.37236/3752","author":[{"first_name":"Catherine","full_name":"Greenhill, Catherine","last_name":"Greenhill"},{"full_name":"Kwan, Matthew Alan","first_name":"Matthew Alan","orcid":"0000-0002-4003-7567","last_name":"Kwan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3"},{"last_name":"Wind","first_name":"David","full_name":"Wind, David"}],"_id":"9594","citation":{"apa":"Greenhill, C., Kwan, M. A., &#38; Wind, D. (2014). On the number of spanning trees in random regular graphs. <i>The Electronic Journal of Combinatorics</i>. The Electronic Journal of Combinatorics. <a href=\"https://doi.org/10.37236/3752\">https://doi.org/10.37236/3752</a>","ista":"Greenhill C, Kwan MA, Wind D. 2014. On the number of spanning trees in random regular graphs. The Electronic Journal of Combinatorics. 21(1), P1.45.","chicago":"Greenhill, Catherine, Matthew Alan Kwan, and David Wind. “On the Number of Spanning Trees in Random Regular Graphs.” <i>The Electronic Journal of Combinatorics</i>. The Electronic Journal of Combinatorics, 2014. <a href=\"https://doi.org/10.37236/3752\">https://doi.org/10.37236/3752</a>.","ieee":"C. Greenhill, M. A. Kwan, and D. Wind, “On the number of spanning trees in random regular graphs,” <i>The Electronic Journal of Combinatorics</i>, vol. 21, no. 1. The Electronic Journal of Combinatorics, 2014.","ama":"Greenhill C, Kwan MA, Wind D. On the number of spanning trees in random regular graphs. <i>The Electronic Journal of Combinatorics</i>. 2014;21(1). doi:<a href=\"https://doi.org/10.37236/3752\">10.37236/3752</a>","mla":"Greenhill, Catherine, et al. “On the Number of Spanning Trees in Random Regular Graphs.” <i>The Electronic Journal of Combinatorics</i>, vol. 21, no. 1, P1.45, The Electronic Journal of Combinatorics, 2014, doi:<a href=\"https://doi.org/10.37236/3752\">10.37236/3752</a>.","short":"C. Greenhill, M.A. Kwan, D. Wind, The Electronic Journal of Combinatorics 21 (2014)."},"date_created":"2021-06-23T06:29:35Z","month":"02","article_processing_charge":"No","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","oa":1,"status":"public","external_id":{"arxiv":["1309.6710"]}}