{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:45:45Z","timestamp":1759063545158,"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>An edge-weighting vertex colouring of a graph is an edge-weight assignment such that the accumulated weights at the vertices yield a proper vertex colouring.  If such an assignment from a set $S$ exists, we say the graph is $S$-weight colourable. We consider the $S$-weight colourability of digraphs by defining the accumulated weight at a vertex to be the sum of the inbound weights minus the sum of the outbound weights.  Bartnicki et al. showed that every digraph is $S$-weight colourable for any set $S$ of size $2$ and asked whether one could show the same result using an algebraic approach.  Using the Combinatorial Nullstellensatz and a classical theorem of Schur, we provide such a solution.<\/jats:p>","DOI":"10.37236\/508","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:56:54Z","timestamp":1578715014000},"source":"Crossref","is-referenced-by-count":5,"title":["Digraphs are $2$-Weight Choosable"],"prefix":"10.37236","volume":"18","author":[{"given":"Mahdad","family":"Khatirinejad","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Reza","family":"Naserasr","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mike","family":"Newman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ben","family":"Seamone","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Brett","family":"Stevens","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,1,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p21\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p21\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:17:46Z","timestamp":1579303066000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,1,19]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/508","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,1,19]]},"article-number":"P21"}}