{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T06:46:06Z","timestamp":1769841966076,"version":"3.49.0"},"reference-count":13,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2017,12,8]],"date-time":"2017-12-08T00:00:00Z","timestamp":1512691200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006606","name":"Natural Science Foundation of Tianjin City","doi-asserted-by":"publisher","award":["17JCQNJC00300"],"award-info":[{"award-number":["17JCQNJC00300"]}],"id":[{"id":"10.13039\/501100006606","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[2018,8]]},"abstract":"Abstract<\/jats:title>The star chromatic index<\/jats:italic> of a multigraph G<\/jats:italic>, denoted , is the minimum number of colors needed to properly color the edges of G<\/jats:italic> such that no path or cycle of length four is bicolored. A multigraph G<\/jats:italic> is star<\/jats:italic> k<\/jats:italic>\u2010edge\u2010colorable<\/jats:italic> if . Dvo\u0159\u00e1k, Mohar, and \u0160\u00e1mal [Star chromatic index, J. Graph Theory<\/jats:italic> 72<\/jats:bold> (2013), 313\u2013326] proved that every subcubic multigraph is star 7\u2010edge\u2010colorable. They conjectured in the same article that every subcubic multigraph should be star 6\u2010edge\u2010colorable. In this article, we first prove that it is NP\u2010complete to determine whether for an arbitrary graph G<\/jats:italic>. This answers a question of Mohar. We then establish some structure results on subcubic multigraphs G<\/jats:italic> with such that but for any , where . We finally apply the structure results, along with a simple discharging method, to prove that every subcubic multigraph G<\/jats:italic> is star 6\u2010edge\u2010colorable if , and star 5\u2010edge\u2010colorable if , respectively, where is the maximum average degree of a multigraph G<\/jats:italic>. This partially confirms the conjecture of Dvo\u0159\u00e1k, Mohar, and \u0160\u00e1mal.<\/jats:p>","DOI":"10.1002\/jgt.22230","type":"journal-article","created":{"date-parts":[[2017,12,8]],"date-time":"2017-12-08T05:06:58Z","timestamp":1512709618000},"page":"566-576","source":"Crossref","is-referenced-by-count":19,"title":["Star chromatic index of subcubic multigraphs"],"prefix":"10.1002","volume":"88","author":[{"given":"Hui","family":"Lei","sequence":"first","affiliation":[{"name":"Center for Combinatorics and LPMC Nankai University Tianjin 300071 China"}]},{"given":"Yongtang","family":"Shi","sequence":"additional","affiliation":[{"name":"Center for Combinatorics and LPMC Nankai University Tianjin 300071 China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6183-0110","authenticated-orcid":false,"given":"Zi\u2010Xia","family":"Song","sequence":"additional","affiliation":[{"name":"Department of Mathematics University of Central Florida Orlando FL 32816 USA"}]}],"member":"311","published-online":{"date-parts":[[2017,12,8]]},"reference":[{"key":"e_1_2_6_2_1","doi-asserted-by":"crossref","first-page":"#R26","DOI":"10.37236\/1779","article-title":"Coloring with no 2\u2010colored P\n 4's","volume":"11","author":"Albertson M. O.","year":"2004","journal-title":"Electron. J. Combin."},{"key":"e_1_2_6_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.21862"},{"key":"e_1_2_6_4_1","unstructured":"S.Kerdjoudj A. V.Kostochka andA.Raspaud List star edge coloring of subcubic graphs to appear in Discuss. Math. Graph Theory."},{"key":"e_1_2_6_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(98)00393-8"},{"key":"e_1_2_6_6_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.20392"},{"key":"e_1_2_6_7_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.21636"},{"key":"e_1_2_6_8_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.21644"},{"key":"e_1_2_6_9_1","doi-asserted-by":"publisher","DOI":"10.1137\/0210055"},{"key":"e_1_2_6_10_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.20342"},{"key":"e_1_2_6_11_1","first-page":"94","article-title":"An upper bound on the star chromatic index of graphs with","volume":"44","author":"Liu X.\u2010S.","year":"2008","journal-title":"J. Lanzhou Univ. (Nat. 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