{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:29Z","timestamp":1753893809472,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The notion of pattern hypergraph provides a unified view of several previously studied coloring concepts. A pattern hypergraph $H$ is a hypergraph where each edge is assigned a type $\\Pi_i$ that determines which of possible colorings of the edge are proper. A vertex coloring of $H$ is proper if it is proper for every edge. In general, the set of integers $k$ such that $H$ can be properly colored with exactly $k$ colors need not be an interval.  We find a simple sufficient and necessary condition on the edge types $\\Pi_1,\\ldots,\\Pi_\\lambda$ for the existence of a pattern hypergraph $H$ with edges of types $\\Pi_1,\\ldots,\\Pi_\\lambda$ such that the numbers of colors in proper colorings of $H$ do not form an interval of integers.<\/jats:p>","DOI":"10.37236\/287","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:17:45Z","timestamp":1578716265000},"source":"Crossref","is-referenced-by-count":5,"title":["Pattern Hypergraphs"],"prefix":"10.37236","volume":"17","author":[{"given":"Zden\u011bk","family":"Dvo\u0159\u00e1k","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jan","family":"K\u00e1ra","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel","family":"Kr\u00e1l'","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ond\u0159ej","family":"Pangr\u00e1c","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2010,1,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r15\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r15\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T00:02:11Z","timestamp":1579305731000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/287","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2010,1,14]]},"article-number":"R15"}}