{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:33Z","timestamp":1753893813631,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A hypergraph is properly 2-colorable if each vertex can be colored by one of two colors and no edge is completely colored by a single color. We present a complete algebraic characterization of the 2-colorability of r-uniform hypergraphs. This generalizes a well known algebraic characterization of k-colorability of graphs due to Alon, Tarsi, Lovasz, de Loera, and Hillar. We also introduce a method for distinguishing proper 2-colorings called coloring schemes, and provide a decomposition of all proper 2-colorings into these schemes. As an application, we present a new example of a 4-uniform non-2-colorable hypergraph on 11 vertices and 24 edges which is not isomorphic to a well-known construction by Seymour (1974) of a minimal non-2-colorable 4-uniform hypergraph. Additionally, we provide a heuristically constructed hypergraph which admits only specific coloring schemes. Further, we give an algebraic characterization of the coloring scheme known as a conflict-free coloring.<\/jats:p>","DOI":"10.37236\/8205","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T02:04:33Z","timestamp":1578621873000},"source":"Crossref","is-referenced-by-count":0,"title":["2-Colorability of r-Uniform Hypergraphs"],"prefix":"10.37236","volume":"26","author":[{"given":"Michael","family":"Krul","sequence":"first","affiliation":[]},{"given":"Lubo\u0161","family":"Thoma","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,8,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i3p30\/7890","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i3p30\/7890","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:09:49Z","timestamp":1579216189000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i3p30"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,16]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,7,4]]}},"URL":"https:\/\/doi.org\/10.37236\/8205","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,8,16]]},"article-number":"P3.30"}}