{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T09:48:55Z","timestamp":1648979335279},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2014,3]]},"abstract":"<jats:p> In 2004, Karo\u0144ski, \u0141uczak, and Thomason conjectured that the edges of any connected graph on at least 3 vertices may be weighted from the set {1, 2, 3} so that the vertices are properly colored by the sums of their incident edge weights. Bartnicki, Grytczuk and Niwcyk introduced its list version. Assign to each edge e \u2208 E(G) a list of k real numbers, say L(e), and choose a weight w(e) \u2208 L(e) for each e \u2208 E(G). The resulting function w : E(G) \u2192 \u22c3<jats:sub>e\u2208E(G)<\/jats:sub> L(e) is called an edge k-list-weighting. Given a graph G, the smallest k such that any assignment of lists of size k to E(G) permits an edge k-list-weighting which is a vertex coloring by sums is denoted by [Formula: see text] and called the edge weight choosability of G. Bartnicki, Grytczuk and Niwcyk conjectured that if G is a nice graph (without a component isomorphic to K<jats:sub>2<\/jats:sub>), then [Formula: see text]. There is no known constant K such that [Formula: see text] for any nice graph G. Ben Seamone proved that [Formula: see text] for any nice graph G with maximum degree \u0394(G) by using Alon's Combinatorial Nullstellensatz. In this paper, we improve this bound to [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s1793830914500104","type":"journal-article","created":{"date-parts":[[2013,10,31]],"date-time":"2013-10-31T00:59:09Z","timestamp":1383181149000},"page":"1450010","source":"Crossref","is-referenced-by-count":2,"title":["A NOTE ON EDGE WEIGHT CHOOSABILITY OF GRAPHS"],"prefix":"10.1142","volume":"06","author":[{"given":"JINGCHENG","family":"FU","sequence":"first","affiliation":[{"name":"School of Mathematics, Shandong University, Jinan, 250100, P. R. China"}]},{"given":"GUANGHUI","family":"WANG","sequence":"additional","affiliation":[{"name":"School of Mathematics, Shandong University, Jinan, 250100, P. R. China"}]},{"given":"JIANLIANG","family":"WU","sequence":"additional","affiliation":[{"name":"School of Mathematics, Shandong University, Jinan, 250100, P. R. China"}]},{"given":"JIN","family":"XU","sequence":"additional","affiliation":[{"name":"School of Mathematics, Shandong University, Jinan, 250100, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2014,2,18]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548398003411"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.20354"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"rf4","first-page":"125","volume":"12","author":"Czerwi\u0144ski S.","journal-title":"Combinatorica"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-010-0952-7"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2009.06.002"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2003.12.001"},{"key":"rf8","first-page":"1","volume":"14","author":"Khatirinejad M.","journal-title":"Discrete Math. Theoret. Comp. Sci."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830914500104","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T17:59:27Z","timestamp":1565114367000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830914500104"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,2,18]]},"references-count":8,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2014,2,18]]},"published-print":{"date-parts":[[2014,3]]}},"alternative-id":["10.1142\/S1793830914500104"],"URL":"https:\/\/doi.org\/10.1142\/s1793830914500104","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,2,18]]}}}