منابع مشابه
A stochastic Ramsey theorem
A stochastic extension of Ramsey’s theorem is established. Any Markov chain generates a filtration relative to which one may define a notion of stopping time. A stochastic colouring is any fc-valued (k < oo) colour func tion defined on all pairs consisting of a bounded stopping time and a finite partial history of the chain truncated before this stopping time. For any bounded stopping time 6 a...
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Let c(m, zi) be the least integer p such that, for any graph G of order p, either G has an zzi-cycle or its complement G has an zz-cycle. Values of c(m, n) are established for zzz, zi < 6 and general formulas are proved for c(3, zi), c(4, n), and c(5, zz). Introduction. It is a well-known fact that in any gathering of six people, there are three people who are mutual acquaintances or three peop...
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We give a lower bound for the Ramsey number and the planar Ramsey number for C4 and complete graphs. We prove that the Ramsey number for C4 and K7 is 21 or 22. Moreover we prove that the planar Ramsey number for C4 and K6 is equal to 17.
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The goal of these notes is to give a proof of the Dual Ramsey Theorem. This theorem was first proved in “A Dual Form of Ramsey’s Theorem” by Tim Carlson and Steve Simpson, Advances in Mathematics, 1984. The proof presented here is the same proof given in the paper and follows much of the same notation and terminology. The main change is that we will explicitly use the notion of “infinite variab...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2012
ISSN: 0012-365X
DOI: 10.1016/j.disc.2011.11.022