{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:41:11Z","timestamp":1760150471882,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,11,22]],"date-time":"2023-11-22T00:00:00Z","timestamp":1700611200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Research, Development and Innovation Office, NKFIH","award":["SNN 129364","FK 132060"],"award-info":[{"award-number":["SNN 129364","FK 132060"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In a finite mathematical structure with a given partition, a substructure is said to be gregarious if either it meets each partition class or it shares at most one element with each partition class. In this paper, we considered edge decompositions of graphs and hypergraphs into gregarious subgraphs and subhypergraphs. We mostly dealt with \u201ccomplete equipartite\u201d graphs and hypergraphs, where the vertex classes have the same size and precisely those edges or hyperedges of a fixed cardinality are present that do not contain more than one element from any class. Some related graph classes generated by product operations were also considered. The generalization to hypergraphs offers a wide open area for further research.<\/jats:p>","DOI":"10.3390\/sym15122097","type":"journal-article","created":{"date-parts":[[2023,11,22]],"date-time":"2023-11-22T03:54:37Z","timestamp":1700625277000},"page":"2097","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Gregarious Decompositions of Complete Equipartite Graphs and Related Structures"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3235-9221","authenticated-orcid":false,"given":"Zsolt","family":"Tuza","sequence":"first","affiliation":[{"name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Re\u00e1ltanoda Str. 13-15, 1053 Budapest, Hungary"},{"name":"Faculty of Information Technology, University of Pannonia, Egyetem Str. 10, 8200 Veszpr\u00e9m, Hungary"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,22]]},"reference":[{"key":"ref_1","unstructured":"(2023, July 23). 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