{"title":"Splitting matchings and the Ryser-Brualdi-Stein conjecture for multisets","oa":1,"ddc":["510"],"tmp":{"short":"CC BY-ND (4.0)","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"},"intvolume":"        30","external_id":{"arxiv":["2212.03100"]},"date_published":"2023-07-28T00:00:00Z","doi":"10.37236/11714","ec_funded":1,"article_processing_charge":"Yes","citation":{"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>","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.","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>.","short":"M. Anastos, D. Fabian, A. Müyesser, T. Szabó, Electronic Journal of Combinatorics 30 (2023)."},"article_type":"original","quality_controlled":"1","has_accepted_license":"1","abstract":[{"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.","lang":"eng"}],"publisher":"Electronic Journal of Combinatorics","file_date_updated":"2023-09-15T08:02:09Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","license":"https://creativecommons.org/licenses/by-nd/4.0/","day":"28","volume":30,"year":"2023","publication_identifier":{"eissn":["1077-8926"]},"issue":"3","language":[{"iso":"eng"}],"date_updated":"2023-09-15T08:12:30Z","date_created":"2023-09-10T22:01:12Z","publication_status":"published","project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","grant_number":"101034413"}],"file":[{"content_type":"application/pdf","checksum":"52c46c8cb329f9aaee9ade01525f317b","success":1,"file_id":"14338","creator":"dernst","access_level":"open_access","date_updated":"2023-09-15T08:02:09Z","date_created":"2023-09-15T08:02:09Z","file_name":"2023_elecJournCombinatorics_Anastos.pdf","relation":"main_file","file_size":247917}],"month":"07","scopus_import":"1","article_number":"P3.10","oa_version":"Published Version","_id":"14319","status":"public","publication":"Electronic Journal of Combinatorics","author":[{"last_name":"Anastos","full_name":"Anastos, Michael","first_name":"Michael","id":"0b2a4358-bb35-11ec-b7b9-e3279b593dbb"},{"last_name":"Fabian","full_name":"Fabian, David","first_name":"David"},{"first_name":"Alp","last_name":"Müyesser","full_name":"Müyesser, Alp"},{"last_name":"Szabó","full_name":"Szabó, Tibor","first_name":"Tibor"}],"department":[{"_id":"MaKw"}],"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)."}