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74.562  Articles
1 of 7.457 pages  |  10  records  |  more records»
In this paper we improve the upper bound on the multi-color Ramsey numbers of paths and even cycles. More precisely, we prove the following. For every r=2r\geq 2 there exists an n0=n0(r)n_0=n_0(r) such that for n=n0n\geq n_0 we have Rr... see more

Burr, Erdos, Faudree, Rousseau and Schelp initiated the study of Ramsey numbers of trees versus odd cycles, proving that R(Tn,Cm)=2n-1R(T_n, C_m) = 2n - 1 for all odd m=3m \ge 3 and n=756m10n \ge 756m^{10}, where TnT_n is a tree with nn vertices and CmC_m... see more

Let s and k be positive integers with k = 2 and G1, G2, …, Gk be simple graphs. The set multipartite Ramsey number, denoted by Ms(G1, G2, …, Gk), is the smallest positive integer c such that any&... see more

For various connected simple graphs G, we extend the table of diagonal graph Ramsey numbers R(G, G) in ‘An Atlas of Graphs.’ This is accomplished by first converting the calculation of R(G, G) into a satisfiability problem in prop... see more

Let Kn be a complete graph with n vertices. For graphs G and H, the Ramsey number R(G, H) is the smallest positive integer n such that in every red-blue coloring on the edges of Kn, there is a re... see more

For the Ramsey number r(Tn, Bm), where Tn denotes a tree of order n and Bm denotes the m-page book K2 + bar(K)m, it is known that r(Tn, Bm)=2n - 1 if n = 3m - 3. In case of n < 3m - 3,&nb... see more

Abstract: Let the star on n vertices, namely K1, n - 1 be denoted by Sn. If every two coloring of the edges of a complete balanced multipartite graph Kj × s there is a copy of Sn in the first color or a copy of... see more

This paper seeks to develop the multicolor version of star-critical Ramsey numbers, which serve as a measure of the strength of the corresponding Ramsey numbers.  We offer several general theorems, some of which focus on Ramsey-good cases (i.e., case... see more

Harary and Miller (1983) started the research on the (restricted) size Ramsey number for a pair of small graphs. They obtained the values for some pairs of small graphs with order not more than four. In the same year, Faudree and Sheehan continued the res... see more

1 of 7.457 pages  |  10  records  |  more records»