{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T08:03:47Z","timestamp":1769155427055,"version":"3.49.0"},"reference-count":9,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p> A 2-distance coloring of a graph is a proper [Formula: see text]-coloring in which any two vertices with distance at most two get different colors. The 2-distance number is the smallest number [Formula: see text] such that [Formula: see text] has a 2-distance [Formula: see text]-coloring, denoted as [Formula: see text]. In 1977, Wegner conjectured that for each planar graph [Formula: see text] with maximum degree [Formula: see text], [Formula: see text] if [Formula: see text], [Formula: see text] if [Formula: see text], and [Formula: see text] if [Formula: see text]. In 2001, Thomassen supported the conjecture by proving the case [Formula: see text]. The conjecture is still open even for [Formula: see text]. In this paper, we show that [Formula: see text] for the case [Formula: see text] which improves the upper bound 18 recently obtained by Hou et\u00a0al. <\/jats:p>","DOI":"10.1142\/s1793830924300029","type":"journal-article","created":{"date-parts":[[2024,4,9]],"date-time":"2024-04-09T08:10:08Z","timestamp":1712650208000},"source":"Crossref","is-referenced-by-count":1,"title":["2-Distance coloring of planar graphs with maximum degree 5"],"prefix":"10.1142","volume":"17","author":[{"given":"Ming","family":"Chen","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-0370-119X","authenticated-orcid":false,"given":"Lu","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Min","family":"Wang","sequence":"additional","affiliation":[{"name":"Kewen College, Jiangsu Normal University, Xuzhou, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shan","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,5,10]]},"reference":[{"key":"S1793830924300029BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2022.113288"},{"key":"S1793830924300029BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2021.112766"},{"key":"S1793830924300029BIB004","doi-asserted-by":"publisher","DOI":"10.1137\/0405048"},{"key":"S1793830924300029BIB005","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.10077"},{"key":"S1793830924300029BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-023-02615-1"},{"key":"S1793830924300029BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2004.12.005"},{"key":"S1793830924300029BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2017.08.010"},{"key":"S1793830924300029BIB010","series-title":"Technical Report","volume-title":"Graphs with Given Diameter and a Coloring Problem","author":"Wegner G.","year":"1977"},{"key":"S1793830924300029BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/s10878-018-0285-7"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830924300029","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,22]],"date-time":"2025-01-22T00:59:01Z","timestamp":1737507541000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793830924300029"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,10]]},"references-count":9,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["10.1142\/S1793830924300029"],"URL":"https:\/\/doi.org\/10.1142\/s1793830924300029","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,5,10]]},"article-number":"2430002"}}