{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T10:15:08Z","timestamp":1770286508976,"version":"3.49.0"},"reference-count":14,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,1,25]],"date-time":"2006-01-25T00:00:00Z","timestamp":1138147200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[2006,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Jeager et al. introduced a concept of group connectivity as a generalization of nowhere zero flows and its dual concept group coloring, and conjectured that every 5\u2010edge connected graph is Z<jats:sub>3<\/jats:sub>\u2010connected. For planar graphs, this is equivalent to that every planar graph with girth at least 5 must have group chromatic number at most 3. In this article, we show that if <jats:italic>G<\/jats:italic> is a plane graph with girth at least 4 such that all 4 cycles are independent, every 4\u2010cycle is a facial cycle and the distance between every pair of a 4\u2010cycle and a 5\u2010cycle is at least 1, then the group chromatic number of <jats:italic>G<\/jats:italic> is at most 3. As a special case, we show that the conjecture above holds for planar graphs. We also prove that if <jats:italic>G<\/jats:italic> is a connected <jats:italic>K<\/jats:italic><jats:sub>3,3<\/jats:sub>\u2010minor free graph with girth at least 5, then the group chromatic number is at most 3. \u00a9 2006 Wiley Periodicals, Inc. J Graph Theory 52: 51\u201372, 2006<\/jats:p>","DOI":"10.1002\/jgt.20147","type":"journal-article","created":{"date-parts":[[2006,1,25]],"date-time":"2006-01-25T23:21:02Z","timestamp":1138231262000},"page":"51-72","source":"Crossref","is-referenced-by-count":11,"title":["Group chromatic number of planar graphs of girth at least 4"],"prefix":"10.1002","volume":"52","author":[{"given":"Hong\u2010Jian","family":"Lai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiangwen","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,1,25]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"e_1_2_1_3_2","first-page":"123","article-title":"Group coloring and group connectivity of graphs","volume":"134","author":"Chen Z. 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