{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T20:03:56Z","timestamp":1773691436530,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A strong edge-coloring of a graph $G$ is a coloring of the edges such that every color class induces a matching in $G$. The strong chromatic index of a graph is the minimum number of colors needed in a strong edge-coloring of the graph. In 1985, Erd\u0151s and Ne\u0161et\u0159il conjectured that every graph with maximum degree $\\Delta$ has a strong edge-coloring using at most $\\frac{5}{4}\\Delta^2$ colors if $\\Delta$ is even, and at most $\\frac{5}{4}\\Delta^2 - \\frac{1}{2}\\Delta + \\frac{1}{4}$ if $\\Delta$ is odd. Despite recent progress for large $\\Delta$ by using an iterative probabilistic argument, the only nontrivial case of the conjecture that has been verified is when $\\Delta = 3$, leaving the need for new approaches to verify the conjecture for any $\\Delta\\ge 4$. In this paper, we apply some ideas used in previous results to an upper bound of 21 for graphs with maximum degree 4, which improves a previous bound due to Cranston in 2006 and moves closer to the conjectured upper bound of 20.<\/jats:p>","DOI":"10.37236\/7016","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:10:49Z","timestamp":1578669049000},"source":"Crossref","is-referenced-by-count":32,"title":["Strong Chromatic Index of Graphs With Maximum Degree Four"],"prefix":"10.37236","volume":"25","author":[{"given":"Mingfang","family":"Huang","sequence":"first","affiliation":[]},{"given":"Michael","family":"Santana","sequence":"additional","affiliation":[]},{"given":"Gexin","family":"Yu","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,8,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i3p31\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i3p31\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:26:53Z","timestamp":1579235213000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i3p31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,24]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2018,7,12]]}},"URL":"https:\/\/doi.org\/10.37236\/7016","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8,24]]},"article-number":"P3.31"}}