{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:08Z","timestamp":1753893848157,"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>Let $P$ denote a 3-uniform hypergraph consisting of 7 vertices $a,b,c,d,e,f,g$ and 3 edges\u00a0$\\{a,b,c\\}, \\{c,d,e\\},$ and $\\{e,f,g\\}$. It is known that the $r$-colored Ramsey number for $P$ is\u00a0$R(P;r)=r+6$ for $r=2,3$, and that $R(P;r)\\le 3r$ for all $r\\ge3$. The latter result follows by a\u00a0standard application of the Tur\u00e1n number $\\mathrm{ex}_3(n;P)$, which was determined to be $\\binom{n-1}2$\u00a0in our previous work. We have also shown that the full star is the only extremal 3-graph for $P$.\u00a0In this paper, we perform a subtle analysis of the Tur\u00e1n numbers for $P$ under some additional\u00a0restrictions. Most importantly, we determine the largest number of edges in an $n$-vertex $P$-free\u00a03-graph which is not a star. These Tur\u00e1n-type results, in turn, allow us to confirm the formula\u00a0$R(P;r)=r+6$ for $r\\in\\{4,5,6,7\\}$.<\/jats:p>","DOI":"10.37236\/7119","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:51:16Z","timestamp":1578671476000},"source":"Crossref","is-referenced-by-count":4,"title":["Multicolor Ramsey Numbers and Restricted Tur\u00e1n Numbers for the Loose 3-Uniform Path of Length Three"],"prefix":"10.37236","volume":"24","author":[{"given":"Andrzej","family":"Ruci\u0144ski","sequence":"first","affiliation":[]},{"given":"Eliza","family":"Jackowska","sequence":"additional","affiliation":[]},{"given":"Joanna","family":"Polcyn","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,7,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i3p5\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i3p5\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:51:11Z","timestamp":1579236671000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i3p5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,14]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,7,14]]}},"URL":"https:\/\/doi.org\/10.37236\/7119","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,7,14]]},"article-number":"P3.5"}}