{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T12:32:33Z","timestamp":1759667553137,"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>A colorful path in a graph $G$ is a path with $\\chi(G)$ vertices whose colors are different. A $v$-colorful path is such a path, starting from $v$. Let $G\\neq C_7$ be a connected graph with maximum degree $\\Delta(G)$. We show that there exists a $(\\Delta(G)+1)$-coloring of $G$ with a $v$-colorful path for every $v\\in V(G)$. We also prove that this result is true if one replaces $(\\Delta(G)+1)$ colors with $2\\chi(G)$ colors. If $\\chi(G)=\\omega(G)$, then the result still holds for $\\chi(G)$ colors. For every graph $G$, we show that there exists a $\\chi(G)$-coloring of $G$ with a rainbow path of length $\\lfloor\\chi(G)\/2\\rfloor$ starting from each $v \\in V(G)$.<\/jats:p>","DOI":"10.37236\/504","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:57:04Z","timestamp":1578715024000},"source":"Crossref","is-referenced-by-count":12,"title":["Colorful Paths in Vertex Coloring of Graphs"],"prefix":"10.37236","volume":"18","author":[{"given":"Saieed","family":"Akbari","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vahid","family":"Liaghat","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Afshin","family":"Nikzad","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,1,12]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p17\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p17\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:17:56Z","timestamp":1579303076000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,1,12]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/504","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,1,12]]},"article-number":"P17"}}