{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:20:11Z","timestamp":1759335611926,"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\u00a0majority coloring of a digraph is a coloring of its vertices such that for each vertex $v$, at most half of the out-neighbors of $v$ have the same color as $v$. A digraph $D$ is majority $k$-choosable if for any assignment of lists of colors of size $k$ to the vertices there is a majority coloring of $D$ from these lists. We prove that every digraph is majority $4$-choosable. This gives a positive answer to a question posed recently by Kreutzer, Oum, Seymour, van der Zypen, and Wood (2017). We obtain this result as a consequence of a more general theorem, in which majority condition is profitably extended. For instance, the theorem implies also that every digraph has a coloring from arbitrary lists of size three, in which at most $2\/3$ of the out-neighbors of any vertex share its color. This solves another problem posed by the same authors, and supports an intriguing conjecture stating that every digraph is majority $3$-colorable.<\/jats:p>","DOI":"10.37236\/6923","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:45:28Z","timestamp":1578671128000},"source":"Crossref","is-referenced-by-count":6,"title":["Majority Choosability of Digraphs"],"prefix":"10.37236","volume":"24","author":[{"given":"Marcin","family":"Anholcer","sequence":"first","affiliation":[]},{"given":"Bart\u0142omiej","family":"Bosek","sequence":"additional","affiliation":[]},{"given":"Jaros\u0142aw","family":"Grytczuk","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,9,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i3p57\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i3p57\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:45:45Z","timestamp":1579236345000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i3p57"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,22]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,7,14]]}},"URL":"https:\/\/doi.org\/10.37236\/6923","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,9,22]]},"article-number":"P3.57"}}