Add to ORKGWe discuss some computational challenges and related open questions concerning classical Ramsey numbers. This talk overviews known constructive bounds for the difference between consecutive Ramsey numbers and presents what is known about the most studied cases including $R(5,5)$ and $R(3,3,4)$. Although the main problems we discuss are concerned with concrete cases, and they involve significant computational approaches, there are interesting and important theoretical questions behind each of them
The Ramsey number $R(F,H)$ is the minimum number $N$ such that any $N$-vertex graph either contains ...
We give an exponential improvement to the lower bound on diagonal Ramsey numbers for any fixed numbe...
Using computer algorithms we establish that the Ramsey number R(3, K-10 - e) is equal to 37, which s...
Using computational techniques we derive six new upper bounds on the classical two-color Ramsey numb...
We discuss some computational challenges and related open questions concerning classical Ramsey numb...
The Ramsey number $R(r, b)$ is the least positive integer such that every edge 2-coloring of the com...
Ramsey theory is a eld of study named after the mathematician Frank P. Ramsey. In general, problems ...
Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-colouring...
For graphs G_1,G_2,...,G_m the Ramsey number R(G_1,G_2,...,G_m) is defined to be the smallest intege...
We discuss some of our favorite open questions about Ramsey numbers and a related problem on edge Fo...
AbstractSome computer programs used to generate Ramsey edge colorings of graphs are described. New r...
Establishing the values of Ramsey numbers is, in general, a difficult task from the computational po...
Ramsey theory studies the existence of highly regular patterns in large sets of objects. Given two g...
AbstractConsidering a known upper bound, the exact value of the Ramsey number r(K2,2,K3,n) is determ...
AbstractUsing methods developed by Graver and Yackel, and various computer algorithms, we show that ...
The Ramsey number $R(F,H)$ is the minimum number $N$ such that any $N$-vertex graph either contains ...
We give an exponential improvement to the lower bound on diagonal Ramsey numbers for any fixed numbe...
Using computer algorithms we establish that the Ramsey number R(3, K-10 - e) is equal to 37, which s...
Using computational techniques we derive six new upper bounds on the classical two-color Ramsey numb...
We discuss some computational challenges and related open questions concerning classical Ramsey numb...
The Ramsey number $R(r, b)$ is the least positive integer such that every edge 2-coloring of the com...
Ramsey theory is a eld of study named after the mathematician Frank P. Ramsey. In general, problems ...
Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-colouring...
For graphs G_1,G_2,...,G_m the Ramsey number R(G_1,G_2,...,G_m) is defined to be the smallest intege...
We discuss some of our favorite open questions about Ramsey numbers and a related problem on edge Fo...
AbstractSome computer programs used to generate Ramsey edge colorings of graphs are described. New r...
Establishing the values of Ramsey numbers is, in general, a difficult task from the computational po...
Ramsey theory studies the existence of highly regular patterns in large sets of objects. Given two g...
AbstractConsidering a known upper bound, the exact value of the Ramsey number r(K2,2,K3,n) is determ...
AbstractUsing methods developed by Graver and Yackel, and various computer algorithms, we show that ...
The Ramsey number $R(F,H)$ is the minimum number $N$ such that any $N$-vertex graph either contains ...
We give an exponential improvement to the lower bound on diagonal Ramsey numbers for any fixed numbe...
Using computer algorithms we establish that the Ramsey number R(3, K-10 - e) is equal to 37, which s...