منابع مشابه
The planar Ramsey number PR(K4-e, K5)
The planar Ramsey number PR (H1, H2) is the smallest integer n such that any planar graph on n vertices contains a copy of H1 or its complement contains a copy of H2. It is known that the Ramsey number R(K4 − e, K6) = 21, and the planar Ramsey numbers PR(K4 − e, Kl) for l ≤ 5 are known. In this paper, we give the lower bounds on PR (K4 − e, Kl) and determine the exact value of PR (K4 − e, K6).
متن کاملThe Ramsey Multiplicity of K4
With the help of computer algorithms, we improve the lower bound on the Ramsey multiplicity of K4, and thus show that the exact value of it is equal to 9. The Ramsey multiplicity M(G) of a graph G is defined as the smallest number of monochromatic copies ofG in any two-coloring of edges of KR(G), whereR(G) is the Ramsey number of G, i.e. the smallest integer n such that any two-coloring of edge...
متن کاملThree-Color Ramsey Numbers For Paths
We prove for sufficiently large n the following conjecture of Faudree and Schelp : R(Pn, Pn, Pn) = { 2n− 1 for odd n, 2n− 2 for even n, for the three-color Ramsey numbers of paths on n vertices. ∗2000 Mathematics Subject Classification: 05C55, 05C38. The second author was supported in part by OTKA Grants T038198 and T046234.
متن کاملOn Some Three-Color Ramsey Numbers
In this paper we study three-color Ramsey numbers. Let Ki,j denote a complete i by j bipartite graph. We shall show that (i) for any connected graphs G1, G2 and G3, if r(G1, G2) ≥ s(G3), then r(G1, G2, G3) ≥ (r(G1, G2) − 1)(χ(G3) − 1) + s(G3), where s(G3) is the chromatic surplus of G3; (ii)(k + m − 2)(n − 1) + 1 ≤ r(K1,k,K1,m,Kn) ≤ (k + m − 1)(n − 1) + 1, and if k or m is odd, the second inequ...
متن کاملThe value of the Ramsey number R(Cn, K4) is 3(n-1)+1 (n≥4)
The Ramsey number R(Cn, Km) is the smallest integer p such that any graph G on p vertices either contains a cycle Cn with length n or contains an independent set with order m. In this paper we prove that R(Cn , K 4 ) = 3(n 1) + 1 (n ~ 4). We shall only consider graphs without multiple edges or loops. The Ramsey number R(Cn,Km) is the smallest integer p such that any graph G on p vertices either...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1991
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90122-i