{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T11:25:20Z","timestamp":1769599520346,"version":"3.49.0"},"reference-count":19,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,8,21]],"date-time":"2021-08-21T00:00:00Z","timestamp":1629504000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100018818","name":"National Research, Development and Innovation Office","doi-asserted-by":"publisher","award":["SNN 129364"],"award-info":[{"award-number":["SNN 129364"]}],"id":[{"id":"10.13039\/501100018818","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Ministry of Innovation and Technology NRDI Office","award":["AINL Program"],"award-info":[{"award-number":["AINL Program"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we investigate partitions of highly symmetrical discrete structures called cycloids. In general, a mixed hypergraph has two types of hyperedges. The vertices are colored in such a way that each C-edge has two vertices of the same color, and each D-edge has two vertices of distinct colors. In our case, a mixed cycloid is a mixed hypergraph whose vertices can be arranged in a cyclic order, and every consecutive p vertices form a C-edge, and every consecutive q vertices form a D-edge in the ordering. We completely determine the maximum number of colors that can be used for any p\u22653 and any q\u22652. We also develop an algorithm that generates a coloring with any number of colors between the minimum and maximum. Finally, we discuss the colorings of mixed cycloids when the maximum number of colors coincides with its upper bound, which is the largest cardinality of a set of vertices containing no C-edge.<\/jats:p>","DOI":"10.3390\/sym13081539","type":"journal-article","created":{"date-parts":[[2021,8,22]],"date-time":"2021-08-22T23:00:09Z","timestamp":1629673209000},"page":"1539","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Coloring Properties of Mixed Cycloids"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4909-6694","authenticated-orcid":false,"given":"Gy\u00f6rgy","family":"D\u00f3sa","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Pannonia, Egyetem Str. 10, 8200 Veszpr\u00e9m, Hungary"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7692-0039","authenticated-orcid":false,"given":"Nicholas","family":"Newman","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Troy University, 600 University Ave., Troy, AL 36082, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3235-9221","authenticated-orcid":false,"given":"Zsolt","family":"Tuza","sequence":"additional","affiliation":[{"name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Re\u00e1ltanoda Str. 13\u201315, 1053 Budapest, Hungary"},{"name":"Department of Computer Science and Systems Technology, University of Pannonia, Egyetem Str. 10, 8200 Veszpr\u00e9m, Hungary"}]},{"given":"Vitaly","family":"Voloshin","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Troy University, 600 University Ave., Troy, AL 36082, USA"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1843","DOI":"10.1016\/B978-0-12-823377-1.50308-6","article-title":"Modelling circular structures in reaction networks: Petri nets and reaction network flux analysis","volume":"48","author":"Weber","year":"2020","journal-title":"Comput. 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Combin."},{"key":"ref_19","first-page":"97","article-title":"About perfection of circular mixed hypergraphs","volume":"76","author":"Newman","year":"2021","journal-title":"Le Mat."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/8\/1539\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:48:36Z","timestamp":1760165316000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/8\/1539"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,21]]},"references-count":19,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2021,8]]}},"alternative-id":["sym13081539"],"URL":"https:\/\/doi.org\/10.3390\/sym13081539","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,21]]}}}