{"oa":1,"abstract":[{"text":"A graph G=(V, E) is called fully regular if for every independent set I c V, the number of vertices in V\\I  that are not connected to any element of I depends only on the size of I. A linear ordering of the vertices of G is called successive if for every i, the first i vertices induce a connected subgraph of G. We give an explicit formula for the number of successive vertex orderings of a fully regular graph.\r\nAs an application of our results, we give alternative proofs of two theorems of Stanley and Gao & Peng, determining the number of linear edge orderings of complete graphs and complete bipartite graphs, respectively, with the property that the first i edges induce a connected subgraph.\r\nAs another application, we give a simple product formula for the number of linear orderings of the hyperedges of a complete 3-partite 3-uniform hypergraph such that, for every i, the first i hyperedges induce a connected subgraph. We found similar formulas for complete (non-partite) 3-uniform hypergraphs and in another closely related case, but we managed to verify them only when the number of vertices is small.","lang":"eng"}],"year":"2023","author":[{"full_name":"Fang, Lixing","last_name":"Fang","first_name":"Lixing"},{"full_name":"Huang, Hao","last_name":"Huang","first_name":"Hao"},{"first_name":"János","last_name":"Pach","full_name":"Pach, János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"},{"first_name":"Gábor","last_name":"Tardos","full_name":"Tardos, Gábor"},{"first_name":"Junchi","last_name":"Zuo","full_name":"Zuo, Junchi"}],"day":"01","language":[{"iso":"eng"}],"has_accepted_license":"1","article_number":"105776","tmp":{"short":"CC BY-NC-SA (4.0)","image":"/images/cc_by_nc_sa.png","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode"},"citation":{"ista":"Fang L, Huang H, Pach J, Tardos G, Zuo J. 2023. Successive vertex orderings of fully regular graphs. Journal of Combinatorial Theory. Series A. 199(10), 105776.","mla":"Fang, Lixing, et al. “Successive Vertex Orderings of Fully Regular Graphs.” <i>Journal of Combinatorial Theory. Series A</i>, vol. 199, no. 10, 105776, Elsevier, 2023, doi:<a href=\"https://doi.org/10.1016/j.jcta.2023.105776\">10.1016/j.jcta.2023.105776</a>.","apa":"Fang, L., Huang, H., Pach, J., Tardos, G., &#38; Zuo, J. (2023). Successive vertex orderings of fully regular graphs. <i>Journal of Combinatorial Theory. Series A</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jcta.2023.105776\">https://doi.org/10.1016/j.jcta.2023.105776</a>","chicago":"Fang, Lixing, Hao Huang, János Pach, Gábor Tardos, and Junchi Zuo. “Successive Vertex Orderings of Fully Regular Graphs.” <i>Journal of Combinatorial Theory. Series A</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.jcta.2023.105776\">https://doi.org/10.1016/j.jcta.2023.105776</a>.","ama":"Fang L, Huang H, Pach J, Tardos G, Zuo J. Successive vertex orderings of fully regular graphs. <i>Journal of Combinatorial Theory Series A</i>. 2023;199(10). doi:<a href=\"https://doi.org/10.1016/j.jcta.2023.105776\">10.1016/j.jcta.2023.105776</a>","short":"L. Fang, H. Huang, J. Pach, G. Tardos, J. Zuo, Journal of Combinatorial Theory. Series A 199 (2023).","ieee":"L. Fang, H. Huang, J. Pach, G. Tardos, and J. Zuo, “Successive vertex orderings of fully regular graphs,” <i>Journal of Combinatorial Theory. Series A</i>, vol. 199, no. 10. Elsevier, 2023."},"intvolume":"       199","title":"Successive vertex orderings of fully regular graphs","article_processing_charge":"Yes (in subscription journal)","publication_identifier":{"eissn":["1096-0899"],"issn":["0097-3165"]},"ddc":["510"],"scopus_import":"1","volume":199,"date_published":"2023-10-01T00:00:00Z","quality_controlled":"1","publisher":"Elsevier","license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","external_id":{"arxiv":["2206.13592"]},"month":"10","date_created":"2023-06-25T22:00:45Z","publication_status":"published","issue":"10","publication":"Journal of Combinatorial Theory. Series A","doi":"10.1016/j.jcta.2023.105776","oa_version":"Published Version","department":[{"_id":"HeEd"}],"date_updated":"2024-01-30T12:03:51Z","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file_date_updated":"2024-01-30T12:03:10Z","file":[{"relation":"main_file","file_id":"14902","content_type":"application/pdf","checksum":"9eebc213b4182a66063a99083ff5bd04","file_name":"2023_JourCombinatiorialTheory_Fang.pdf","date_created":"2024-01-30T12:03:10Z","file_size":352555,"access_level":"open_access","creator":"dernst","success":1,"date_updated":"2024-01-30T12:03:10Z"}],"_id":"13165","status":"public","article_type":"original"}