A variation of a classical Turán-type extremal problem

On a Ramsey-Turán type problem

Denote by I(G) the maximal number of independent points in a graph G and let or(G) = I(G), where G is the complement of G. Thus a(G) is the maximal p for which G contains a K, , a complete graph with p vertices. Denote byf(n, k, 1) the maximal m for which there is a graph with n points and m edges such that or(G) < k and I(G) < I. The function f(n, k, I) was introduced and investigated by Erdii...

the investigation of the relationship between type a and type b personalities and quality of translation

چکیده ندارد.

Turán - type Problems in Extremal Combinatorics Adam Marcus

A Ramsey-type problem and the Turán numbers

For each n and k, we examine bounds on the largest number m so that for any k-coloring of the edges of Kn there exists a copy of Km whose edges receive at most k − 1 colors. We show that for k ≥ √ n+ Ω(n), the largest value of m is asymptotically equal to the Turán number t(n, b ( n 2 ) /kc), while for any constant > 0, if k ≤ (1 − ) √ n then the largest m is asymptotically larger than that Tur...

The critical window for the classical Ramsey-Turán problem

The first application of Szemerédi’s powerful regularity method was the following celebrated Ramsey-Turán result proved by Szemerédi in 1972: any K4-free graph on n vertices with independence number o(n) has at most ( 18 +o(1))n 2 edges. Four years later, Bollobás and Erdős gave a surprising geometric construction, utilizing the isoperimetric inequality for the high dimensional sphere, of a K4-...