{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:48:37Z","timestamp":1759063717541},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2012,6]]},"abstract":"<jats:p> An injective k-coloring of a graph G is an assignment of k colors to the vertices of G so that any two vertices with a common neighbor receive distinct colors, and \u03c7<jats:sub>i<\/jats:sub>(G) is the injective chromatic number of G. Dimitrov et al. proved \u03c7<jats:sub>i<\/jats:sub>(G) \u2264 \u0394(G) + 2 for a planar graph G with g(G) \u2265 7. In this paper, we show that if G is a planar graph with g(G) \u2265 7 and \u0394(G) \u2265 7, then \u03c7<jats:sub>i<\/jats:sub>(G) \u2264 \u0394(G) + 1. <\/jats:p>","DOI":"10.1142\/s1793830912500346","type":"journal-article","created":{"date-parts":[[2012,6,19]],"date-time":"2012-06-19T14:55:53Z","timestamp":1340117753000},"page":"1250034","source":"Crossref","is-referenced-by-count":10,"title":["INJECTIVE COLORING OF PLANAR GRAPHS WITH GIRTH 7"],"prefix":"10.1142","volume":"04","author":[{"given":"YUEHUA","family":"BU","sequence":"first","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Zhejiang, Jinhua 321004, China"}]},{"given":"KAI","family":"LU","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Zhejiang, Jinhua 321004, China"}]}],"member":"219","published-online":{"date-parts":[[2012,6,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2010.10.008"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1134\/S0037446606010034"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2008.08.016"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-010-9425-x"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2010.07.003"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2009.04.020"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(01)00466-6"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2008.04.005"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830912500346","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T22:42:23Z","timestamp":1565131343000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830912500346"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6]]},"references-count":8,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2012,6,21]]},"published-print":{"date-parts":[[2012,6]]}},"alternative-id":["10.1142\/S1793830912500346"],"URL":"https:\/\/doi.org\/10.1142\/s1793830912500346","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6]]}}}