{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:23Z","timestamp":1753893863546,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $p$ and $q$ be positive integers such that $1 \\leq q \\leq {p \\choose 2}$. A $(p,q)$-coloring of the complete graph on $n$ vertices $K_n$ is an edge coloring for which every $p$-clique contains edges of at least $q$ distinct colors. We denote the minimum number of colors needed for such a $(p,q)$-coloring of $K_n$ by $f(n,p,q)$. This is known as the Erd\u00f6s-Gy\u00e1rf\u00e1s function. In this paper we give an explicit $(5,6)$-coloring with $n^{1\/2+o(1)}$ colors. This improves the best known upper bound of $f(n,5,6)=O\\left(n^{3\/5}\\right)$ given by\u00a0Erd\u00f6s and Gy\u00e1rf\u00e1s, and comes close to matching the order of the best known lower bound, $f(n,5,6) = \\Omega\\left(n^{1\/2}\\right)$.<\/jats:p>","DOI":"10.37236\/7852","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T01:05:00Z","timestamp":1578618300000},"source":"Crossref","is-referenced-by-count":1,"title":["An Explicit Edge-Coloring of $K_n$ with Six Colors on Every $K_5$"],"prefix":"10.37236","volume":"26","author":[{"given":"Alex","family":"Cameron","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,10,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i4p13\/7938","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i4p13\/7938","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:08:05Z","timestamp":1579216085000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i4p13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,11]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,10,11]]}},"URL":"https:\/\/doi.org\/10.37236\/7852","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,10,11]]},"article-number":"P4.13"}}