منابع مشابه
New lower bounds for hypergraph Ramsey numbers
The Ramsey number rk(s, n) is the minimum N such that for every red-blue coloring of the k-tuples of {1, . . . , N}, there are s integers such that every k-tuple among them is red, or n integers such that every k-tuple among them is blue. We prove the following new lower bounds for 4-uniform hypergraph Ramsey numbers: r4(5, n) > 2 n log n and r4(6, n) > 2 2 1/5 , where c is an absolute positive...
متن کاملNew Upper Bounds for Ramsey Numbers
The problem of determining Ramsey numbers is known to be very difficult. The few known exact values and several bounds for different G1, G2 or m, n are scattered among many technical papers (see [3]). A graph G with order p is called a (G1,G2; p)-graph ((m, n; p)-graph, resp.) if G does not contain a G1 and Ḡ does not contain a G2 (Km and Kn , resp.). It is easy to see that R(G1,G2) = p0 +1 iff...
متن کاملLuus-Jaakola Optimization Procedure for Ramsey Number Lower Bounds
Ramsey numbers have been widely studied for decades, but the exact values for all but a handful are still unknown. In recent years, optimization algorithms have proven useful in calculating lower bounds for certain Ramsey numbers. In this paper, we define an optimization algorithm based on the Luus-Jaakola procedure to calculate Ramsey number lower bounds. We demonstrate the effectiveness of th...
متن کاملSome lower bounds for the $L$-intersection number of graphs
For a set of non-negative integers~$L$, the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v subseteq {1,dots, l}$ to vertices $v$, such that every two vertices $u,v$ are adjacent if and only if $|A_u cap A_v|in L$. The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the ver...
متن کاملThe Ramsey Number for Hypergraph
Let Cn denote the 3-uniform hypergraph loose cycle, that is the hypergraph with vertices v1, . . . , vn and edges v1v2v3, v3v4v5, v5v6v7, . . . , vn−1vnv1. We prove that every red-blue colouring of the edges of the complete 3-uniform hypergraph with N vertices contains a monochromatic copy of Cn, where N is asymptotically equal to 5n/4. Moreover this result is (asymptotically) best possible.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2013
ISSN: 0012-365X
DOI: 10.1016/j.disc.2013.07.022