{"date_updated":"2024-01-30T12:03:51Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","short":"CC BY-NC-SA (4.0)","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","image":"/images/cc_by_nc_sa.png"},"title":"Successive vertex orderings of fully regular graphs","type":"journal_article","intvolume":"       199","article_type":"original","citation":{"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>.","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>.","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.","short":"L. Fang, H. Huang, J. Pach, G. Tardos, J. Zuo, Journal of Combinatorial Theory. Series A 199 (2023).","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>","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.","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>"},"doi":"10.1016/j.jcta.2023.105776","file_date_updated":"2024-01-30T12:03:10Z","year":"2023","department":[{"_id":"HeEd"}],"quality_controlled":"1","abstract":[{"lang":"eng","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."}],"issue":"10","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":199,"date_created":"2023-06-25T22:00:45Z","ddc":["510"],"scopus_import":"1","publication":"Journal of Combinatorial Theory. Series A","_id":"13165","day":"01","status":"public","language":[{"iso":"eng"}],"external_id":{"arxiv":["2206.13592"]},"license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","oa_version":"Published Version","file":[{"date_created":"2024-01-30T12:03:10Z","content_type":"application/pdf","file_size":352555,"file_id":"14902","file_name":"2023_JourCombinatiorialTheory_Fang.pdf","date_updated":"2024-01-30T12:03:10Z","relation":"main_file","access_level":"open_access","creator":"dernst","checksum":"9eebc213b4182a66063a99083ff5bd04","success":1}],"publisher":"Elsevier","author":[{"full_name":"Fang, Lixing","first_name":"Lixing","last_name":"Fang"},{"last_name":"Huang","first_name":"Hao","full_name":"Huang, Hao"},{"last_name":"Pach","first_name":"János","full_name":"Pach, János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"},{"full_name":"Tardos, Gábor","first_name":"Gábor","last_name":"Tardos"},{"first_name":"Junchi","full_name":"Zuo, Junchi","last_name":"Zuo"}],"article_processing_charge":"Yes (in subscription journal)","date_published":"2023-10-01T00:00:00Z","has_accepted_license":"1","publication_status":"published","article_number":"105776","publication_identifier":{"eissn":["1096-0899"],"issn":["0097-3165"]},"month":"10"}