New lower bounds for Ramsey number R (p, q; 4)
نویسندگان
چکیده
منابع مشابه
A New Lower Bound for the Ramsey Number R(4, 8)
The lower bound for the classical Ramsey number R(4, 8) is improved from 56 to 58. The author has found a new edge coloring of K57 that has no complete graphs of order 4 in the first color, and no complete graphs of order 8 in the second color. The coloring was found using a SAT solver which is based on MiniSat and customized for solving Ramsey problems. Recently Exoo improved the lower bound f...
متن کاملNew 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 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 کاملNew Computational Upper Bounds for Ramsey Numbers R(3, k)
Using computational techniques we derive six new upper bounds on the classical twocolor Ramsey numbers: R(3, 10) ≤ 42, R(3, 11) ≤ 50, R(3, 13) ≤ 68, R(3, 14) ≤ 77, R(3, 15) ≤ 87, and R(3, 16) ≤ 98. All of them are improvements by one over the previously best published bounds. Let e(3, k, n) denote the minimum number of edges in any triangle-free graph on n vertices without independent sets of o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1995
ISSN: 0012-365X
DOI: 10.1016/0012-365x(95)00049-3