These include discussing the asymptotic behavior of f(n), considering what happens for other weight functions, showing that some natural variants of both problems have simple counterexamples, and presenting a simple coloring that gives a lower bound on Ramsey numbers for cliques with increasing consecutive differences.
Dec 7, 2011 · Abstract:Ramsey's theorem, in the version of Erdős and Szekeres, states that every 2-coloring of the edges of the complete graph on {1, ...
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Abstract. Ramsey's theorem, in the version of Erd˝os and Szekeres, states that every 2-coloring of the edges of the complete graph on ¹1;2;:::;nº contains a ...
Ramsey's theorem, in the version of Erdos and Szekeres, states that every 2-coloring of the edges of the complete graph on {1,2,…,n} contains a ...
Two well-studied extensions of Ramsey's theorem are considered, obtaining an upper bound on n which is exponential in a power of k and improving a result of ...
Let r (k) be the minimum n such that in every 2-coloring of the edges of the complete graph Kn there is a monochromatic Kk. Ramsey's theorem states that r ...
In this article, we consider two well-studied extensions of Ramsey's theorem. Improving a result of Rödl, we show that there is a constant c > 0 such that every ...
An extension of this theorem applies to any finite number of colours, rather than just two. ... The special case above has c = 2 (and n1 = r and n2 = s).
Feb 16, 2001 · In this talk, we consider two well-studied extensions of Ramsey's theorem. Improving a result of Rodl, we show that there is a constant c > 0 ...
Nov 19, 2024 · Ramsey's Theorem states that [ω]2 is a Ramsey family. Is there an uncountable Ramsey family A⊆P(ω) such that [ω]2⊆A?