{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:39Z","timestamp":1753893819124,"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>A $3$-coloring of the elements of an abelian group is said to be rainbow-free if there is no $3$-term arithmetic progression with its members having pairwise distinct colors. We give a structural characterization of rainbow-free colorings of abelian groups. This characterization proves a conjecture of Jungi\u0107 et al. on the size of the smallest chromatic class of a rainbow-free $3$-coloring of cyclic groups.<\/jats:p>","DOI":"10.37236\/2054","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:31:26Z","timestamp":1578713486000},"source":"Crossref","is-referenced-by-count":5,"title":["Rainbow-free $3$-colorings of Abelian Groups"],"prefix":"10.37236","volume":"19","author":[{"given":"Amanda","family":"Montejano","sequence":"first","affiliation":[]},{"given":"Oriol","family":"Serra","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2012,2,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i1p45\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i1p45\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:41:41Z","timestamp":1579300901000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i1p45"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2,23]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2012,2,15]]}},"URL":"https:\/\/doi.org\/10.37236\/2054","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,2,23]]},"article-number":"P45"}}