Let P3denote the path with 3 edges. The Ramsey number r(P3, k), k a natural number, is the minimum number of vertices in a complete graph for which every ...

May 11, 2016 · In this article we study the values of three-color diagonal Ramsey numbers for paths. In the case of two color Ramsey numbers, a well known ...

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Abstract. For graphs G1,G2,G3, the three-color Ramsey number R(G1, G2,G3) is the smallest integer n such that if we arbitrarily color the edges.

Coloring the edges of [A,B], [C,D] by color 1, the edges of [A,D],. [B,C] by color 2, the edges of [A,C], [B,D] by color 3, no matter how the edges inside the ...

The Ramsey number R ( P 3 3 ; n ) is the smallest integer N such that any coloring of the edges of the complete 3-graph on N vertices, K N 3 , with n colors ...

The complete graph on 3 vertices and the cycle of length 3 is the same graph, K3 = C3. The study of K3 in the context of Ramsey numbers is very rich in itself ...

Jul 18, 2019 · We prove that the size-Ramsey number of the 3-uniform tight path on n vertices P^{(3)}_n is linear in n, i.e., \hat{r}_2(P^{(3)}_n) = O(n).

Ramsey's theorem, in one of its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours) of a sufficiently ...

Feb 14, 2017 · Suppose the edges of F is red-blue colored such that three independent edges are red and the rest is blue. Then GF = P6 and GF is exactly ...