{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:40Z","timestamp":1753893820428,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $G$ be a graph. The core of $G$, denoted by $G_{\\Delta}$, is the subgraph of $G$ induced by the vertices of degree $\\Delta(G)$, where $\\Delta(G)$ denotes the maximum degree of $G$. A $k$-edge coloring of $G$ is a function $f:E(G)\\rightarrow L$ such that $|L| = k$ and $f(e_1)\\neq f(e_2)$ for all two adjacent edges\u00a0 $e_1$ and $e_2$ of $G$. The chromatic index of $G$, denoted by $\\chi'(G)$, is the minimum number $k$ for which $G$ has a $k$-edge coloring.\u00a0 A graph $G$ is said to be Class $1$ if $\\chi'(G) = \\Delta(G)$ and Class $2$ if $\\chi'(G) = \\Delta(G) + 1$. In this paper it is shown that every connected graph $G$ of even order and with $\\Delta(G_{\\Delta})\\leq 2$ is Class $1$ if $|G_{\\Delta}|\\leq 9$ or $G_{\\Delta}$ is a cycle of order $10$.<\/jats:p>","DOI":"10.37236\/2101","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:30:59Z","timestamp":1578695459000},"source":"Crossref","is-referenced-by-count":3,"title":["The Chromatic Index of a Graph Whose Core has Maximum Degree $2$"],"prefix":"10.37236","volume":"19","author":[{"given":"Mikio","family":"Kano","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Saieed","family":"Akbari","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maryam","family":"Ghanbari","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammad Javad","family":"Nikmehr","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2012,3,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i1p58\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i1p58\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T17:41:01Z","timestamp":1579282861000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i1p58"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3,19]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2012,2,15]]}},"URL":"https:\/\/doi.org\/10.37236\/2101","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,3,19]]},"article-number":"P58"}}