[{"scopus_import":"1","day":"28","author":[{"id":"0b2a4358-bb35-11ec-b7b9-e3279b593dbb","full_name":"Anastos, Michael","last_name":"Anastos","first_name":"Michael"},{"last_name":"Fabian","full_name":"Fabian, David","first_name":"David"},{"full_name":"Müyesser, Alp","last_name":"Müyesser","first_name":"Alp"},{"last_name":"Szabó","full_name":"Szabó, Tibor","first_name":"Tibor"}],"oa_version":"Published Version","title":"Splitting matchings and the Ryser-Brualdi-Stein conjecture for multisets","volume":30,"date_created":"2023-09-10T22:01:12Z","article_type":"original","has_accepted_license":"1","license":"https://creativecommons.org/licenses/by-nd/4.0/","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","image":"/image/cc_by_nd.png","short":"CC BY-ND (4.0)"},"abstract":[{"lang":"eng","text":"We study multigraphs whose edge-sets are the union of three perfect matchings, M1, M2, and M3. Given such a graph G and any a1; a2; a3 2 N with a1 +a2 +a3 6 n - 2, we show there exists a matching M of G with jM \\ Mij = ai for each i 2 f1; 2; 3g. The bound n - 2 in the theorem is best possible in general. We conjecture however that if G is bipartite, the same result holds with n - 2 replaced by n - 1. We give a construction that shows such a result would be tight. We\r\nalso make a conjecture generalising the Ryser-Brualdi-Stein conjecture with colour\r\nmultiplicities."}],"intvolume":"        30","file_date_updated":"2023-09-15T08:02:09Z","publication_status":"published","publication_identifier":{"eissn":["1077-8926"]},"arxiv":1,"month":"07","department":[{"_id":"MaKw"}],"file":[{"success":1,"file_name":"2023_elecJournCombinatorics_Anastos.pdf","access_level":"open_access","content_type":"application/pdf","relation":"main_file","checksum":"52c46c8cb329f9aaee9ade01525f317b","date_created":"2023-09-15T08:02:09Z","file_size":247917,"creator":"dernst","date_updated":"2023-09-15T08:02:09Z","file_id":"14338"}],"article_number":"P3.10","oa":1,"language":[{"iso":"eng"}],"citation":{"chicago":"Anastos, Michael, David Fabian, Alp Müyesser, and Tibor Szabó. “Splitting Matchings and the Ryser-Brualdi-Stein Conjecture for Multisets.” <i>Electronic Journal of Combinatorics</i>. Electronic Journal of Combinatorics, 2023. <a href=\"https://doi.org/10.37236/11714\">https://doi.org/10.37236/11714</a>.","ista":"Anastos M, Fabian D, Müyesser A, Szabó T. 2023. Splitting matchings and the Ryser-Brualdi-Stein conjecture for multisets. Electronic Journal of Combinatorics. 30(3), P3.10.","mla":"Anastos, Michael, et al. “Splitting Matchings and the Ryser-Brualdi-Stein Conjecture for Multisets.” <i>Electronic Journal of Combinatorics</i>, vol. 30, no. 3, P3.10, Electronic Journal of Combinatorics, 2023, doi:<a href=\"https://doi.org/10.37236/11714\">10.37236/11714</a>.","apa":"Anastos, M., Fabian, D., Müyesser, A., &#38; Szabó, T. (2023). Splitting matchings and the Ryser-Brualdi-Stein conjecture for multisets. <i>Electronic Journal of Combinatorics</i>. Electronic Journal of Combinatorics. <a href=\"https://doi.org/10.37236/11714\">https://doi.org/10.37236/11714</a>","ama":"Anastos M, Fabian D, Müyesser A, Szabó T. Splitting matchings and the Ryser-Brualdi-Stein conjecture for multisets. <i>Electronic Journal of Combinatorics</i>. 2023;30(3). doi:<a href=\"https://doi.org/10.37236/11714\">10.37236/11714</a>","short":"M. Anastos, D. Fabian, A. Müyesser, T. Szabó, Electronic Journal of Combinatorics 30 (2023).","ieee":"M. Anastos, D. Fabian, A. Müyesser, and T. Szabó, “Splitting matchings and the Ryser-Brualdi-Stein conjecture for multisets,” <i>Electronic Journal of Combinatorics</i>, vol. 30, no. 3. Electronic Journal of Combinatorics, 2023."},"issue":"3","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes","doi":"10.37236/11714","publisher":"Electronic Journal of Combinatorics","_id":"14319","date_updated":"2023-09-15T08:12:30Z","type":"journal_article","ddc":["510"],"quality_controlled":"1","year":"2023","external_id":{"arxiv":["2212.03100"]},"publication":"Electronic Journal of Combinatorics","status":"public","project":[{"name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"ec_funded":1,"date_published":"2023-07-28T00:00:00Z","acknowledgement":"Anastos has received funding from the European Union’s Horizon 2020 research and in-novation programme under the Marie Sk lodowska-Curie grant agreement No 101034413.Fabian’s research is supported by the Deutsche Forschungsgemeinschaft (DFG, GermanResearch Foundation) Graduiertenkolleg “Facets of Complexity” (GRK 2434)."},{"language":[{"iso":"eng"}],"oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"chicago":"Anastos, Michael. “A Note on Long Cycles in Sparse Random Graphs.” <i>Electronic Journal of Combinatorics</i>. Electronic Journal of Combinatorics, 2023. <a href=\"https://doi.org/10.37236/11471\">https://doi.org/10.37236/11471</a>.","ista":"Anastos M. 2023. A note on long cycles in sparse random graphs. Electronic Journal of Combinatorics. 30(2), P2.21.","mla":"Anastos, Michael. “A Note on Long Cycles in Sparse Random Graphs.” <i>Electronic Journal of Combinatorics</i>, vol. 30, no. 2, P2.21, Electronic Journal of Combinatorics, 2023, doi:<a href=\"https://doi.org/10.37236/11471\">10.37236/11471</a>.","apa":"Anastos, M. (2023). A note on long cycles in sparse random graphs. <i>Electronic Journal of Combinatorics</i>. Electronic Journal of Combinatorics. <a href=\"https://doi.org/10.37236/11471\">https://doi.org/10.37236/11471</a>","ama":"Anastos M. A note on long cycles in sparse random graphs. <i>Electronic Journal of Combinatorics</i>. 2023;30(2). doi:<a href=\"https://doi.org/10.37236/11471\">10.37236/11471</a>","short":"M. Anastos, Electronic Journal of Combinatorics 30 (2023).","ieee":"M. Anastos, “A note on long cycles in sparse random graphs,” <i>Electronic Journal of Combinatorics</i>, vol. 30, no. 2. Electronic Journal of Combinatorics, 2023."},"issue":"2","arxiv":1,"month":"05","article_number":"P2.21","file":[{"content_type":"application/pdf","access_level":"open_access","file_name":"2023_JourCombinatorics_Anastos.pdf","success":1,"checksum":"6269ed3b3eded6536d3d9d6baad2d5b9","relation":"main_file","creator":"dernst","date_updated":"2023-05-22T07:43:19Z","date_created":"2023-05-22T07:43:19Z","file_size":448736,"file_id":"13046"}],"department":[{"_id":"MaKw"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"license":"https://creativecommons.org/licenses/by/4.0/","intvolume":"        30","abstract":[{"text":"Let Lc,n denote the size of the longest cycle in G(n, c/n),c >1 constant.  We show that there exists a continuous function f(c) such that Lc,n/n→f(c) a.s.  for c>20,  thus  extending  a  result  of  Frieze  and  the  author  to  smaller  values  of c. Thereafter,  for c>20,  we  determine  the  limit  of  the  probability  that G(n, c/n)contains  cycles  of  every  length  between  the  length  of  its  shortest  and  its  longest cycles as n→∞.","lang":"eng"}],"has_accepted_license":"1","file_date_updated":"2023-05-22T07:43:19Z","publication_identifier":{"eissn":["1077-8926"]},"publication_status":"published","title":"A note on long cycles in sparse random graphs","oa_version":"Published Version","day":"05","scopus_import":"1","author":[{"first_name":"Michael","id":"0b2a4358-bb35-11ec-b7b9-e3279b593dbb","full_name":"Anastos, Michael","last_name":"Anastos"}],"date_created":"2023-05-21T22:01:05Z","article_type":"original","volume":30,"status":"public","publication":"Electronic Journal of Combinatorics","acknowledgement":"We would like to thank the reviewers for their helpful comments and remarks.","date_published":"2023-05-05T00:00:00Z","external_id":{"isi":["000988285500001"],"arxiv":["2105.13828"]},"year":"2023","isi":1,"ddc":["510"],"quality_controlled":"1","publisher":"Electronic Journal of Combinatorics","article_processing_charge":"No","doi":"10.37236/11471","type":"journal_article","_id":"13042","date_updated":"2023-08-01T14:44:52Z"},{"date_published":"2022-07-29T00:00:00Z","acknowledgement":"Supported by Austrian Science Fund (FWF): I3747, W1230.","status":"public","publication":"Electronic Journal of Combinatorics","isi":1,"year":"2022","external_id":{"arxiv":["2005.07103"],"isi":["000836200300001"]},"quality_controlled":"1","ddc":["510"],"date_updated":"2023-08-03T12:37:54Z","_id":"11740","type":"journal_article","doi":"10.37236/10607","article_processing_charge":"No","publisher":"Electronic Journal of Combinatorics","issue":"3","citation":{"ieee":"O. Cooley, N. Del Giudice, M. Kang, and P. Sprüssel, “Phase transition in cohomology groups of non-uniform random simplicial complexes,” <i>Electronic Journal of Combinatorics</i>, vol. 29, no. 3. Electronic Journal of Combinatorics, 2022.","short":"O. Cooley, N. Del Giudice, M. Kang, P. Sprüssel, Electronic Journal of Combinatorics 29 (2022).","ama":"Cooley O, Del Giudice N, Kang M, Sprüssel P. Phase transition in cohomology groups of non-uniform random simplicial complexes. <i>Electronic Journal of Combinatorics</i>. 2022;29(3). doi:<a href=\"https://doi.org/10.37236/10607\">10.37236/10607</a>","apa":"Cooley, O., Del Giudice, N., Kang, M., &#38; Sprüssel, P. (2022). Phase transition in cohomology groups of non-uniform random simplicial complexes. <i>Electronic Journal of Combinatorics</i>. Electronic Journal of Combinatorics. <a href=\"https://doi.org/10.37236/10607\">https://doi.org/10.37236/10607</a>","mla":"Cooley, Oliver, et al. “Phase Transition in Cohomology Groups of Non-Uniform Random Simplicial Complexes.” <i>Electronic Journal of Combinatorics</i>, vol. 29, no. 3, P3.27, Electronic Journal of Combinatorics, 2022, doi:<a href=\"https://doi.org/10.37236/10607\">10.37236/10607</a>.","chicago":"Cooley, Oliver, Nicola Del Giudice, Mihyun Kang, and Philipp Sprüssel. “Phase Transition in Cohomology Groups of Non-Uniform Random Simplicial Complexes.” <i>Electronic Journal of Combinatorics</i>. Electronic Journal of Combinatorics, 2022. <a href=\"https://doi.org/10.37236/10607\">https://doi.org/10.37236/10607</a>.","ista":"Cooley O, Del Giudice N, Kang M, Sprüssel P. 2022. Phase transition in cohomology groups of non-uniform random simplicial complexes. Electronic Journal of Combinatorics. 29(3), P3.27."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"language":[{"iso":"eng"}],"department":[{"_id":"MaKw"}],"article_number":"P3.27","file":[{"file_size":1768663,"date_created":"2022-08-08T06:28:52Z","date_updated":"2022-08-08T06:28:52Z","creator":"dernst","file_id":"11742","file_name":"2022_ElecJournCombinatorics_Cooley.pdf","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"057c676dcee70236aa234d4ce6138c69"}],"month":"07","arxiv":1,"publication_identifier":{"eissn":["1077-8926"]},"publication_status":"published","file_date_updated":"2022-08-08T06:28:52Z","has_accepted_license":"1","intvolume":"        29","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","image":"/image/cc_by_nd.png","short":"CC BY-ND (4.0)"},"abstract":[{"lang":"eng","text":"We consider a generalised model of a random simplicial complex, which arises from a random hypergraph. Our model is generated by taking the downward-closure of a non-uniform binomial random hypergraph, in which for each k, each set of k+1 vertices forms an edge with some probability pk independently. As a special case, this contains an extensively studied model of a (uniform) random simplicial complex, introduced by Meshulam and Wallach [Random Structures & Algorithms 34 (2009), no. 3, pp. 408–417].\r\nWe consider a higher-dimensional notion of connectedness on this new model according to the vanishing of cohomology groups over an arbitrary abelian group R. We prove that this notion of connectedness displays a phase transition and determine the threshold. We also prove a hitting time result for a natural process interpretation, in which simplices and their downward-closure are added one by one. In addition, we determine the asymptotic behaviour of cohomology groups inside the critical window around the time of the phase transition."}],"volume":29,"article_type":"original","date_created":"2022-08-07T22:01:59Z","author":[{"first_name":"Oliver","full_name":"Cooley, Oliver","id":"43f4ddd0-a46b-11ec-8df6-ef3703bd721d","last_name":"Cooley"},{"full_name":"Del Giudice, Nicola","last_name":"Del Giudice","first_name":"Nicola"},{"full_name":"Kang, Mihyun","last_name":"Kang","first_name":"Mihyun"},{"first_name":"Philipp","full_name":"Sprüssel, Philipp","last_name":"Sprüssel"}],"day":"29","scopus_import":"1","title":"Phase transition in cohomology groups of non-uniform random simplicial complexes","oa_version":"Published Version"},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"short":"O. Cooley, M. Kang, J. Zalla, The Electronic Journal of Combinatorics 29 (2022).","ieee":"O. Cooley, M. Kang, and J. Zalla, “Loose cores and cycles in random hypergraphs,” <i>The Electronic Journal of Combinatorics</i>, vol. 29, no. 4. The Electronic Journal of Combinatorics, 2022.","ama":"Cooley O, Kang M, Zalla J. Loose cores and cycles in random hypergraphs. <i>The Electronic Journal of Combinatorics</i>. 2022;29(4). doi:<a href=\"https://doi.org/10.37236/10794\">10.37236/10794</a>","mla":"Cooley, Oliver, et al. “Loose Cores and Cycles in Random Hypergraphs.” <i>The Electronic Journal of Combinatorics</i>, vol. 29, no. 4, P4.13, The Electronic Journal of Combinatorics, 2022, doi:<a href=\"https://doi.org/10.37236/10794\">10.37236/10794</a>.","apa":"Cooley, O., Kang, M., &#38; Zalla, J. (2022). Loose cores and cycles in random hypergraphs. <i>The Electronic Journal of Combinatorics</i>. The Electronic Journal of Combinatorics. <a href=\"https://doi.org/10.37236/10794\">https://doi.org/10.37236/10794</a>","chicago":"Cooley, Oliver, Mihyun Kang, and Julian Zalla. “Loose Cores and Cycles in Random Hypergraphs.” <i>The Electronic Journal of Combinatorics</i>. The Electronic Journal of Combinatorics, 2022. <a href=\"https://doi.org/10.37236/10794\">https://doi.org/10.37236/10794</a>.","ista":"Cooley O, Kang M, Zalla J. 2022. Loose cores and cycles in random hypergraphs. The Electronic Journal of Combinatorics. 29(4), P4.13."},"issue":"4","language":[{"iso":"eng"}],"oa":1,"file":[{"relation":"main_file","checksum":"00122b2459f09b5ae43073bfba565e94","file_name":"2022_ElecJournCombinatorics_Cooley_Kang_Zalla.pdf","success":1,"content_type":"application/pdf","access_level":"open_access","file_id":"12462","date_created":"2023-01-30T11:45:13Z","file_size":626953,"date_updated":"2023-01-30T11:45:13Z","creator":"dernst"}],"article_number":"P4.13","department":[{"_id":"MaKw"}],"month":"10","file_date_updated":"2023-01-30T11:45:13Z","publication_identifier":{"eissn":["1077-8926"]},"publication_status":"published","intvolume":"        29","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","image":"/image/cc_by_nd.png","short":"CC BY-ND (4.0)"},"abstract":[{"lang":"eng","text":"Inspired by the study of loose cycles in hypergraphs, we define the loose core in hypergraphs as a structurewhich mirrors the close relationship between cycles and $2$-cores in graphs. We prove that in the $r$-uniform binomial random hypergraph $H^r(n,p)$, the order of the loose core undergoes a phase transition at a certain critical threshold and determine this order, as well as the number of edges, asymptotically in the subcritical and supercritical regimes.&#x0D;\r\nOur main tool is an algorithm called CoreConstruct, which enables us to analyse a peeling process for the loose core. By analysing this algorithm we determine the asymptotic degree distribution of vertices in the loose core and in particular how many vertices and edges the loose core contains. As a corollary we obtain an improved upper bound on the length of the longest loose cycle in $H^r(n,p)$."}],"has_accepted_license":"1","date_created":"2023-01-16T10:03:57Z","article_type":"original","volume":29,"title":"Loose cores and cycles in random hypergraphs","oa_version":"Published Version","day":"21","scopus_import":"1","author":[{"id":"43f4ddd0-a46b-11ec-8df6-ef3703bd721d","full_name":"Cooley, Oliver","last_name":"Cooley","first_name":"Oliver"},{"first_name":"Mihyun","full_name":"Kang, Mihyun","last_name":"Kang"},{"first_name":"Julian","full_name":"Zalla, Julian","last_name":"Zalla"}],"date_published":"2022-10-21T00:00:00Z","acknowledgement":"Supported by Austrian Science Fund (FWF): I3747, W1230.","status":"public","publication":"The Electronic Journal of Combinatorics","keyword":["Computational Theory and Mathematics","Geometry and Topology","Theoretical Computer Science","Applied Mathematics","Discrete Mathematics and Combinatorics"],"external_id":{"isi":["000876763300001"]},"isi":1,"year":"2022","quality_controlled":"1","ddc":["510"],"type":"journal_article","_id":"12286","date_updated":"2023-08-04T10:29:18Z","publisher":"The Electronic Journal of Combinatorics","article_processing_charge":"No","doi":"10.37236/10794"},{"oa":1,"language":[{"iso":"eng"}],"pubrep_id":"714","citation":{"apa":"Fulek, R., Kynčl, J., Malinovič, I., &#38; Pálvölgyi, D. (2015). Clustered planarity testing revisited. <i>Electronic Journal of Combinatorics</i>. Electronic Journal of Combinatorics. <a href=\"https://doi.org/10.37236/5002\">https://doi.org/10.37236/5002</a>","mla":"Fulek, Radoslav, et al. “Clustered Planarity Testing Revisited.” <i>Electronic Journal of Combinatorics</i>, vol. 22, no. 4, P4.24, Electronic Journal of Combinatorics, 2015, doi:<a href=\"https://doi.org/10.37236/5002\">10.37236/5002</a>.","ista":"Fulek R, Kynčl J, Malinovič I, Pálvölgyi D. 2015. Clustered planarity testing revisited. Electronic Journal of Combinatorics. 22(4), P4.24.","chicago":"Fulek, Radoslav, Jan Kynčl, Igor Malinovič, and Dömötör Pálvölgyi. “Clustered Planarity Testing Revisited.” <i>Electronic Journal of Combinatorics</i>. Electronic Journal of Combinatorics, 2015. <a href=\"https://doi.org/10.37236/5002\">https://doi.org/10.37236/5002</a>.","ieee":"R. Fulek, J. Kynčl, I. Malinovič, and D. Pálvölgyi, “Clustered planarity testing revisited,” <i>Electronic Journal of Combinatorics</i>, vol. 22, no. 4. Electronic Journal of Combinatorics, 2015.","short":"R. Fulek, J. Kynčl, I. Malinovič, D. Pálvölgyi, Electronic Journal of Combinatorics 22 (2015).","ama":"Fulek R, Kynčl J, Malinovič I, Pálvölgyi D. Clustered planarity testing revisited. <i>Electronic Journal of Combinatorics</i>. 2015;22(4). doi:<a href=\"https://doi.org/10.37236/5002\">10.37236/5002</a>"},"issue":"4","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"11","arxiv":1,"department":[{"_id":"UlWa"}],"article_number":"P4.24 ","file":[{"creator":"system","date_updated":"2020-07-14T12:45:08Z","date_created":"2018-12-12T10:15:03Z","file_size":443655,"file_id":"5120","content_type":"application/pdf","access_level":"open_access","file_name":"IST-2016-714-v1+1_5002-15499-3-PB.pdf","checksum":"40b5920b49ee736694f59f39588ee206","relation":"main_file"}],"has_accepted_license":"1","intvolume":"        22","abstract":[{"lang":"eng","text":"The Hanani-Tutte theorem is a classical result proved for the first time in the 1930s that characterizes planar graphs as graphs that admit a drawing in the plane in which every pair of edges not sharing a vertex cross an even number of times. We generalize this result to clustered graphs with two disjoint clusters, and show that a straightforward extension to flat clustered graphs with three or more disjoint clusters is not possible. For general clustered graphs we show a variant of the Hanani-Tutte theorem in the case when each cluster induces a connected subgraph. Di Battista and Frati proved that clustered planarity of embedded clustered graphs whose every face is incident to at most five vertices can be tested in polynomial time. We give a new and short proof of this result, using the matroid intersection algorithm."}],"file_date_updated":"2020-07-14T12:45:08Z","publication_identifier":{"eissn":["1077-8926"]},"publication_status":"published","scopus_import":"1","day":"13","author":[{"orcid":"0000-0001-8485-1774","first_name":"Radoslav","full_name":"Fulek, Radoslav","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","last_name":"Fulek"},{"last_name":"Kynčl","full_name":"Kynčl, Jan","first_name":"Jan"},{"full_name":"Malinovič, Igor","last_name":"Malinovič","first_name":"Igor"},{"full_name":"Pálvölgyi, Dömötör","last_name":"Pálvölgyi","first_name":"Dömötör"}],"oa_version":"Published Version","title":"Clustered planarity testing revisited","volume":22,"date_created":"2018-12-11T11:53:12Z","article_type":"original","status":"public","publication":"Electronic Journal of Combinatorics","project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"ec_funded":1,"date_published":"2015-11-13T00:00:00Z","acknowledgement":"e research leading to these results has received funding fromthe People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme(FP7/2007-2013) under REA grant agreement no [291734], and ESF Eurogiga project GraDR as GAˇCRGIG/11/E023.","year":"2015","related_material":{"record":[{"id":"10793","status":"public","relation":"earlier_version"}]},"external_id":{"arxiv":["1305.4519"]},"publist_id":"5511","ddc":["514","516"],"quality_controlled":"1","article_processing_charge":"No","doi":"10.37236/5002","publisher":"Electronic Journal of Combinatorics","_id":"1642","date_updated":"2023-02-21T16:03:02Z","type":"journal_article"},{"publication_status":"published","publication_identifier":{"eissn":["1077-8926"]},"abstract":[{"lang":"eng","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."}],"intvolume":"        21","volume":21,"article_type":"original","date_created":"2021-06-23T06:29:35Z","author":[{"first_name":"Catherine","last_name":"Greenhill","full_name":"Greenhill, Catherine"},{"first_name":"Matthew Alan","orcid":"0000-0002-4003-7567","last_name":"Kwan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","full_name":"Kwan, Matthew Alan"},{"last_name":"Wind","full_name":"Wind, David","first_name":"David"}],"scopus_import":"1","day":"28","title":"On the number of spanning trees in random regular graphs","oa_version":"Published Version","issue":"1","citation":{"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>.","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>.","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>","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>","short":"C. Greenhill, M.A. Kwan, D. Wind, The Electronic Journal of Combinatorics 21 (2014).","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."},"user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","oa":1,"language":[{"iso":"eng"}],"article_number":"P1.45","month":"02","arxiv":1,"main_file_link":[{"url":"https://doi.org/10.37236/3752","open_access":"1"}],"quality_controlled":"1","date_updated":"2023-02-23T14:02:12Z","_id":"9594","type":"journal_article","doi":"10.37236/3752","article_processing_charge":"No","publisher":"The Electronic Journal of Combinatorics","date_published":"2014-02-28T00:00:00Z","status":"public","publication":"The Electronic Journal of Combinatorics","extern":"1","year":"2014","external_id":{"arxiv":["1309.6710"]}}]