2 00 4 Remarks on a Paper by Y . Caro and R . Yuster on Turán Problem ( Revised )
نویسنده
چکیده
For a graph F and a function f : N → R, let ef (F ) = ∑ x∈V (F ) f(d(x)) and let exf (n, F ) be the maximum of ef (G) over all F -free graphs G with n vertices. Suppose that f is a non-decreasing function with the property that for any ε > 0 there is δ > 0 such that for any n ≤ m ≤ (1+δ)n we have f(m) ≤ (1+ε)f(n). Under this assumption we prove that the asymptotics of exf (n, F ), where F is a fixed non-bipartite graph and n tends to the infinity, can be computed by considering complete (χ(F ) − 1)-partite graphs only. This research was motivated by a paper of Y. Caro and R. Yuster [Electronic J. Combin., 7 (2000)] who studied the case when f : x 7→ x is a power function.
منابع مشابه
Remarks on a Paper by Y. Caro and R. Yuster on Turán Problem
For a graph F and a real p ≥ 1, let ep(F ) = ∑ x∈V (F ) d(x) and let exp(n, F ) be the maximum of ep(G) over all F -free graphs G with n vertices. We prove the conjecture of Caro and Yuster that exp(n, F ) = (1 + o(1)) ( r − 2 r − 1 p n p+1 for any fixed p ≥ 1 and graph F with chromatic number r ≥ 3. This generalizes the Erdős-Stone Theorem.
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