Over the past 15 years, Ramsey theoretic techniques and concepts have been applied with great success to partially ordered sets. In the last year alone, four new applications of Ramsey theory to posets have produced solutions to some challenging combinatorial problems. First, Kierstead and Trotter showed that dimension for interval orders can be characterized by a single ramsey trail by proving...

Several studies have shown that heat stress caused a deterioration in cognitive performance, and that the magnitude of this deterioration was related to the duration of the exposure to high temperature. Particularly in sustained attention tasks, to which some sports activities could be compared, performance decrements were observed under heat stress, and these decrements became more important w...

The irredundant Ramsey number s = s(m,n) [upper domination Ramsey number u = u(m,n), respectively] is the smallest natural number s [u, respectively] such that in any red-blue edge colouring (R,B) of the complete graph of order s [u, respectively], it holds that IR(B) ≥ m or IR(R) ≥ n [Γ(B) ≥ m or Γ(R) ≥ n, respectively], where Γ and IR denote respectively the upper domination number and the ir...

In the Ramsey theory of graphs, star-critical Gallai-Ramsey numbers serve as a measure strength their corresponding numbers. this paper, we evaluate some classes when arguments are disjoint unions K3-subgraphs. The methods used constructive and in all cases considered, find that removal single edge destroys property.

We discuss classical results of Ramsey theory together with their dynamical counterparts, survey recent developments and formulate some natural open questions and conjectures. Mathematics Subject Classification (2000). Primary 28D15, 05D10; Secondary 37A45, 37B10.

A familyB of sequences has the Ramsey property if for every positive integer k, there exists a least positive integer fB(k) such that for every 2-coloring of f1;2; : : : ; fB(k)g there is a monochromatic k-term member of B. For fixed integers m > 1 and 0 q < m, let Bq(m) be the collection of those increasing sequences of positive integers fx1; : : : ;xkg such that xi+1 xi q(mod m) for 1 i k 1. ...