{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:50:53Z","timestamp":1759063853630,"version":"3.41.2"},"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>In this paper we improve the upper bound on the multi-color Ramsey\u00a0numbers of paths and even cycles. More precisely, we prove the following.\u00a0For every $r\\geq 2$ there exists an $n_0=n_0(r)$\u00a0such that for $n\\geq n_0$ we have\u00a0$$R_r(P_n) \\leq \\left( r - \\frac{r}{16r^3+1} \\right) n.$$\u00a0For every $r\\geq 2$ and even $n$ we have\u00a0$$R_r(C_n) \\leq \\left( r - \\frac{r}{16r^3+1} \\right) n + o(n) \\text{ as }n\\rightarrow \\infty.$$ The main tool is a stability version of the\u00a0Erd\u0151s-Gallai theorem that may be of independent interest.<\/jats:p>","DOI":"10.37236\/5663","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:15:57Z","timestamp":1578687357000},"source":"Crossref","is-referenced-by-count":10,"title":["On the Multi-Colored Ramsey Numbers of Paths and Even Cycles"],"prefix":"10.37236","volume":"23","author":[{"given":"G\u00e1bor N.","family":"S\u00e1rk\u00f6zy","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,9,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i3p53\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i3p53\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:12:02Z","timestamp":1579237922000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i3p53"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,9,30]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2016,7,8]]}},"URL":"https:\/\/doi.org\/10.37236\/5663","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,9,30]]},"article-number":"P3.53"}}