{sl let $[n]={1,dots, n}$ be colored in $k$ colors. a rainbow ap$(k)$ in $[n]$ is a $k$ term arithmetic progression whose elements have different colors. conlon, jungi'{c} and radoiv{c}i'{c} cite{conlon} prove that there exists an equinumerous 4-coloring of $[4n]$ which is rainbow ap(4) free, when $n$ is even. based on their construction, we show that such a coloring of ...

In this paper we investigate colorings of sets avoiding similarly colored subsets. If S is an arbitrary colored set and T is a "xed family of bijections of S to itself, then two subsets A; B ⊆ S are said to be colored similarly with respect to T, if there exists a transformation t ∈T mapping A onto B, and preserving a coloring of A. This general setting covers some well-known topics such as non...

A celebrated result in Ramsey Theory states that the order of magnitude of the trianglecomplete graph Ramsey numbers R(3, t) is t/ log t. In this paper, we consider an analogue of this problem for uniform hypergraphs. A triangle is a hypergraph consisting of edges e, f, g such that |e∩ f | = |f ∩ g| = |g ∩ e| = 1 and e ∩ f ∩ g = ∅. For all r ≥ 2, let R(C3,K t ) be the smallest positive integer ...

An edge-coloring of a graph G with colors 1, 2, . . . , t is an interval t-coloring if all colors are used, and the colors of edges incident to each vertex of G are distinct and form an interval of integers. A graph G is interval colorable if it has an interval t-coloring for some positive integer t. For an interval colorable graph G, W (G) denotes the greatest value of t for which G has an int...

conclusions this study revealed that the administration of 600 μg of intravenous se immediately before induction of anesthesia was safe, but when compared to a placebo, no predominant clinical effects or modifications in the systemic inflammatory response induced by on-pump cabg were observed. results data from a total of 81 patients were analyzed: group s (n = 41) and group c (n = 40). there w...