{"title":"The semi-random tree process","language":[{"iso":"eng"}],"month":"05","intvolume":"       126","day":"01","date_published":"2025-05-01T00:00:00Z","department":[{"_id":"MaKw"}],"scopus_import":"1","OA_type":"green","status":"public","acknowledgement":"We are grateful to Dieter Mitsche for related discussions and to several anonymous referees for multiple useful comments.","date_updated":"2025-09-30T10:28:42Z","type":"journal_article","doi":"10.1016/j.ejc.2025.104120","publication_status":"published","external_id":{"arxiv":["2204.07376 "],"isi":["001420659400001"]},"citation":{"chicago":"Burova, Sofiya, and Lyuben Lichev. “The Semi-Random Tree Process.” <i>European Journal of Combinatorics</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.ejc.2025.104120\">https://doi.org/10.1016/j.ejc.2025.104120</a>.","mla":"Burova, Sofiya, and Lyuben Lichev. “The Semi-Random Tree Process.” <i>European Journal of Combinatorics</i>, vol. 126, 104120, Elsevier, 2025, doi:<a href=\"https://doi.org/10.1016/j.ejc.2025.104120\">10.1016/j.ejc.2025.104120</a>.","ieee":"S. Burova and L. Lichev, “The semi-random tree process,” <i>European Journal of Combinatorics</i>, vol. 126. Elsevier, 2025.","apa":"Burova, S., &#38; Lichev, L. (2025). The semi-random tree process. <i>European Journal of Combinatorics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.ejc.2025.104120\">https://doi.org/10.1016/j.ejc.2025.104120</a>","short":"S. Burova, L. Lichev, European Journal of Combinatorics 126 (2025).","ama":"Burova S, Lichev L. The semi-random tree process. <i>European Journal of Combinatorics</i>. 2025;126. doi:<a href=\"https://doi.org/10.1016/j.ejc.2025.104120\">10.1016/j.ejc.2025.104120</a>","ista":"Burova S, Lichev L. 2025. The semi-random tree process. European Journal of Combinatorics. 126, 104120."},"publication_identifier":{"issn":["0195-6698"]},"volume":126,"year":"2025","oa_version":"Preprint","abstract":[{"lang":"eng","text":"The online semi-random graph process is a one-player game which starts with the empty graph on n vertices. At every round, a player (called Builder) is presented with a vertex v chosen uniformly at random and independently from previous rounds, and constructs an edge of their choice that is incident to v. Inspired by recent advances on the semi-random graph process, we define a family of generalized online semi-random models.\r\nWe analyse a particular instance that shares similar features with the original semi-random graph process and determine the hitting times of the classical graph properties minimum degree k,k-connectivity, containment of a perfect matching, a Hamiltonian cycle and an \r\nH-factor for a fixed graph H possessing an additional tree-like property. Along the way, we derive a few consequences of the famous Aldous-Broder algorithm that may be of independent interest."}],"oa":1,"quality_controlled":"1","OA_place":"repository","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_created":"2025-02-10T09:00:53Z","publication":"European Journal of Combinatorics","arxiv":1,"article_processing_charge":"No","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2204.07376","open_access":"1"}],"publisher":"Elsevier","_id":"19018","author":[{"first_name":"Sofiya","full_name":"Burova, Sofiya","last_name":"Burova"},{"last_name":"Lichev","first_name":"Lyuben","full_name":"Lichev, Lyuben","id":"9aa8388e-d003-11ee-8458-c4c1d7447977"}],"article_number":"104120","article_type":"original","isi":1}