{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:45Z","timestamp":1753893825980,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In this paper we study a generalization of both proper edge-coloring and strong edge-coloring: $k$-intersection edge-coloring, introduced by Muthu, Narayanan and Subramanian. In this coloring, the set $S(v)$ of colors used by edges incident to a vertex $v$ does not intersect $S(u)$ on more than $k$ colors when $u$ and $v$ are adjacent. We provide some sharp upper and lower bounds for $\\chi'_{k\\text{-int}}$ for several classes of graphs. For $l$-degenerate graphs we prove that $\\chi'_{k\\text{-int}}(G)\\leq (l+1)\\Delta -l(k-1)-1$. We improve this bound for subcubic graphs by showing that $\\chi'_{2\\text{-int}}(G)\\leq 6$. We show that calculating $\\chi'_{k\\text{-int}}(K_n)$ for arbitrary values of $k$ and $n$ is related to some problems in combinatorial set theory and we provide bounds that are tight for infinitely many values of $n$. Furthermore, for complete bipartite graphs we prove that $\\chi'_{k\\text{-int}}(K_{n,m}) = \\left\\lceil \\frac{mn}{k}\\right\\rceil$. Finally, we show that computing $\\chi'_{k\\text{-int}}(G)$ is NP-complete for every $k\\geq 1$.An addendum was added to this paper on Jul 4, 2015.<\/jats:p>","DOI":"10.37236\/3529","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:13:16Z","timestamp":1578701596000},"source":"Crossref","is-referenced-by-count":0,"title":["From Edge-Coloring to Strong Edge-Coloring"],"prefix":"10.37236","volume":"22","author":[{"given":"Valentin","family":"Borozan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gerard Jennhwa","family":"Chang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nathann","family":"Cohen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shinya","family":"Fujita","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Narayanan","family":"Narayanan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Reza","family":"Naserasr","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Petru","family":"Valicov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2015,4,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i2p9\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i2p9\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:22:48Z","timestamp":1579256568000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i2p9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4,21]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2015,4,14]]}},"URL":"https:\/\/doi.org\/10.37236\/3529","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,4,21]]},"article-number":"P2.9"}}