{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:10:37Z","timestamp":1753884637820,"version":"3.41.2"},"reference-count":7,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"name":"Tianjin Normal University Research Innovation Project for Postgraduate Students, China","award":["2023KYCX052Z"],"award-info":[{"award-number":["2023KYCX052Z"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Inter. Net."],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:p> Gr\u00f6tzsch proved that every triangle-free planar graph has a proper 3-coloring in 1958. One of the generalizations of it is the one that Steinberg and Tovey obtained: Every triangle-free planar graph has a non-uniform\u00a0[Formula: see text]-coloring [Planar Ramsey numbers, J. Combin. Theory Ser. B 59(2)(1993), 288\u2013296]. Moreover, they proposed the following conjecture: Every planar graph on[Formula: see text]\u00a0vertices with at most one triangle has a non-uniform\u00a0[Formula: see text]-coloring. Here, we affirm the conjecture in the situation that every 2-connected outerplanar graph on [Formula: see text] vertices with at most one triangle has a non-uniform\u00a0[Formula: see text]-coloring by Kempe change. <\/jats:p>","DOI":"10.1142\/s021926592450021x","type":"journal-article","created":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T14:12:07Z","timestamp":1732716727000},"source":"Crossref","is-referenced-by-count":0,"title":["Independent Set, Chromatic Number, Non-Uniform Coloring of 2-Connected Outerplanar Graphs and Beyond"],"prefix":"10.1142","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-5731-6212","authenticated-orcid":false,"given":"Hong","family":"Zhai","sequence":"first","affiliation":[{"name":"College of Mathematical Sciences, Tianjin Normal University, Tianjin 300071, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8423-6197","authenticated-orcid":false,"given":"Xingchao","family":"Deng","sequence":"additional","affiliation":[{"name":"College of Mathematical Sciences, Tianjin Normal University, Tianjin 300071, P. R. China"},{"name":"Institute of Mathematics and Interdisciplinary Sciences, Tianjin Normal University, Tianjin 300071, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2070-8845","authenticated-orcid":false,"given":"Junqing","family":"Cai","sequence":"additional","affiliation":[{"name":"College of Mathematical Sciences, Tianjin Normal University, Tianjin 300071, P. R. China"},{"name":"Institute of Mathematics and Interdisciplinary Sciences, Tianjin Normal University, Tianjin 300071, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2024,11,26]]},"reference":[{"key":"S021926592450021XBIB001","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1993.1070"},{"key":"S021926592450021XBIB002","doi-asserted-by":"publisher","DOI":"10.1307\/mmj\/1028998916"},{"key":"S021926592450021XBIB003","first-page":"109","volume":"8","author":"Gr\u00f6tzsch H.","year":"1958","journal-title":"Halle-Wittenberg Math. Natur. Reihe."},{"key":"S021926592450021XBIB004","first-page":"43","volume":"17","author":"Albertson M.","year":"1976","journal-title":"Congr. Numer."},{"key":"S021926592450021XBIB005","first-page":"3","volume":"26","author":"Aksionov V. A.","year":"1974","journal-title":"Diskretnyi Analiz."},{"key":"S021926592450021XBIB006","doi-asserted-by":"publisher","DOI":"10.2307\/2369235"},{"key":"S021926592450021XBIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2020.05.033"}],"container-title":["Journal of Interconnection Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021926592450021X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T00:24:42Z","timestamp":1746059082000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S021926592450021X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,26]]},"references-count":7,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["10.1142\/S021926592450021X"],"URL":"https:\/\/doi.org\/10.1142\/s021926592450021x","relation":{},"ISSN":["0219-2659","1793-6713"],"issn-type":[{"type":"print","value":"0219-2659"},{"type":"electronic","value":"1793-6713"}],"subject":[],"published":{"date-parts":[[2024,11,26]]},"article-number":"2450021"}}