{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:14:55Z","timestamp":1758824095843},"reference-count":10,"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> An injective-k coloring of a graph G is a mapping cV(G) \u2192 {1, 2, \u2026, k}, such that c(u) \u2260 c(v) for each u, v \u2208 V(G), whenever u, v have a common neighbor in G. If G has an injective-k coloring, then we call that G is injective-k colorable. Call \u03c7<jats:sub>i<\/jats:sub>(G) = min {k | G is injective-k colorable} is the injective chromatic number of G. Assign each vertex v \u2208 V(G) a coloring set L(v), then L = {L(v) | v \u2208 V(G)} is said to be a color list of G. Let L be a color list of G, if G has an injective coloring c such that c(v) \u2208 L(v), \u2200v \u2208 V(G), then we call c an injective L-coloring of G. If for any color list L, such that |L(v)| \u2265 k, G has an injective L-coloring, then G is said to be injective k-choosable. Call [Formula: see text] is injective k-choosable} is the injective chromatic number of G. So far, for the plane graph G of girth g(G) \u2265 5 and maximum degree \u0394(G) \u2265 8, the best result of injective chromatic number is \u03c7<jats:sub>i<\/jats:sub>(G) \u2264 \u0394 + 8. In this paper, for the plane graph G, we proved that [Formula: see text] if girth g(G) \u2265 5 and maximum degree \u0394(G) \u2265 8. <\/jats:p>","DOI":"10.1142\/s1793830914500062","type":"journal-article","created":{"date-parts":[[2013,10,31]],"date-time":"2013-10-31T00:59:09Z","timestamp":1383181149000},"page":"1450006","source":"Crossref","is-referenced-by-count":6,"title":["LIST INJECTIVE COLORING OF PLANAR GRAPHS WITH GIRTH g \u2265 5"],"prefix":"10.1142","volume":"06","author":[{"given":"YUEHUA","family":"BU","sequence":"first","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Zhejiang, Jinhua 321004, China"}]},{"given":"SHENG","family":"YANG","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Zhejiang, Jinhua 321004, China"}]}],"member":"219","published-online":{"date-parts":[[2014,2,18]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(01)00466-6"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2009.04.020"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2008.08.016"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2010.10.008"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-010-9425-x"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1134\/S0037446606010034"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2010.07.003"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2008.04.005"},{"key":"rf10","first-page":"25","volume":"25","author":"Zhu H.-Y.","journal-title":"J. Shangdong Uni. Tech. (Natural Sci. Edn)"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2011.10.029"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830914500062","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T17:59:22Z","timestamp":1565114362000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830914500062"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,2,18]]},"references-count":10,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2014,2,18]]},"published-print":{"date-parts":[[2014,3]]}},"alternative-id":["10.1142\/S1793830914500062"],"URL":"https:\/\/doi.org\/10.1142\/s1793830914500062","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]]}}}