“…Gerbner and Palmer [11,Conjecture 20] conjectured that for every graph H there exists r 0 = r 0 (H) such that H is K r+1 -Turán-good for every r ≥ r 0 (H). This conjecture is known to hold for stars [4], more generally for complete multipartite graphs [11], for paths [10] and for the 5-cycle [16]. In this paper we prove the conjecture holds with r 0 = 300v(H) 9 .…”
Let H be a graph. We show that if r is large enough as a function of H, then the r-partite Turán graph maximizes the number of copies of H among all K r+1 -free graphs on a given number of vertices. This confirms a conjecture of Gerbner and Palmer.
“…Gerbner and Palmer [11,Conjecture 20] conjectured that for every graph H there exists r 0 = r 0 (H) such that H is K r+1 -Turán-good for every r ≥ r 0 (H). This conjecture is known to hold for stars [4], more generally for complete multipartite graphs [11], for paths [10] and for the 5-cycle [16]. In this paper we prove the conjecture holds with r 0 = 300v(H) 9 .…”
Let H be a graph. We show that if r is large enough as a function of H, then the r-partite Turán graph maximizes the number of copies of H among all K r+1 -free graphs on a given number of vertices. This confirms a conjecture of Gerbner and Palmer.
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