{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:46Z","timestamp":1753893826127,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The generalized Tur\u00e1n problem ex$(n,T,F)$ is to determine the maximal number of copies of a graph $T$ that can exist in an $F$-free graph on $n$ vertices. Recently, Gerbner and Palmer noted that the solution to the generalized Tur\u00e1n problem is often the original Tur\u00e1n graph. They gave the name \"$F$-Tur\u00e1n-good\" to graphs $T$ for which, for large enough $n$, the solution to the generalized Tur\u00e1n problem is realized by a Tur\u00e1n graph. They prove that the path graph on two edges, $P_2$, is $K_{r+1}$-Tur\u00e1n-good for all $r \\ge 3$, but they conjecture that the same result should hold for all $P_\\ell$. In this paper, using arguments based in flag algebras, we prove that the path on three edges, $P_3$, is also $K_{r+1}$-Tur\u00e1n-good for all $r \\ge 3$.<\/jats:p>","DOI":"10.37236\/10225","type":"journal-article","created":{"date-parts":[[2021,12,3]],"date-time":"2021-12-03T02:57:37Z","timestamp":1638500257000},"source":"Crossref","is-referenced-by-count":3,"title":["Paths of Length Three are $K_{r+1}$-Tur\u00e1n-Good"],"prefix":"10.37236","volume":"28","author":[{"given":"Kyle","family":"Murphy","sequence":"first","affiliation":[]},{"given":"JD","family":"Nir","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2021,12,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i4p34\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i4p34\/data","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i4p34\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,3]],"date-time":"2021-12-03T03:31:22Z","timestamp":1638502282000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i4p34"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,3]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,10,8]]}},"URL":"https:\/\/doi.org\/10.37236\/10225","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2021,12,3]]},"article-number":"P4.34"}}