Related papers: Computational lower limits on small Ramsey numbers
We give two lower bound formulas for multicolored Ramsey numbers. These formulas improve the bounds for several small multicolored Ramsey numbers.
We present a recursive algorithm for finding good lower bounds for the classical Ramsey numbers. Using notions from this algorithm we then give some results for generalized Schur numbers, which we call Issai numbers.
Using cyclic graphs I give new lower bounds for two color and multicolor Ramsey numbers: R(4,16)>163, R(5,11)>170, R(5,12)>190, R(5,13)>212, R(5,14)>238, R(3,3,9)>117, R(3,3,10)>141 and R(3,3,11)>157. Improving the previous best known…
Ramsey's theorem, concerning the guarantee of certain monochromatic patterns in large enough edge-coloured complete graphs, is a fundamental result in combinatorial mathematics. In this work, we highlight the connection between this…
The purpose of this survey is to provide a gentle introduction to several recent breakthroughs in graph Ramsey theory. In particular, we will outline the proofs (due to various groups of authors) of exponential improvements to the diagonal,…
We give a simple proof of the recent remarkable exponential improvement for Ramsey lower bounds, obtained by Ma, Shen and Xie. Our key ingredient is an alternative construction based on Gaussian random graphs, which allows us to simplify…
Circulant graphs have been used to effectively establish lower bounds on many classical Ramsey numbers. Here, we construct circulant graphs of prime order that sharpen the best published lower bounds on two Ramsey numbers. Generalizing…
We give an exponential improvement to the lower bound on diagonal Ramsey numbers for any fixed number of colors greater than two.
The known lower bound for the the classical Ramsey number $R(5,6)$ is improved from $58$ to $59$. The method used to construct the graph is a simple variant of computational methods that have been previously used to construct Ramsey graphs.…
We use finite fields and extend a result of Fan Chung to give eight new, nontrivial, lower bounds.
This technical note aims at evaluating an asymptotic lower bound on abelian Ramsey lengths.
The two-colour Ramsey number $R(m,n)$ is the least natural number $p$ such that any graph of order $p$ must contain either a clique of size $m$ or an independent set of size $n$. We exhibit a method for computing upper bounds for $R(m,n)$…
We give a coding based perspective, on a result of Erd\'{o}s, on a lower bound for the diagonal ramsey numbers.
Lower bounds for some explicit decision problems over the complex numbers are given.
Computing the number of realizations of a minimally rigid graph is a notoriously difficult problem. Towards this goal, for graphs that are minimally rigid in the plane, we take advantage of a recently published algorithm, which is the…
Building upon previous works by Conlon-Ferber and Wigderson, Sawin showed a few years ago that upper bounds on the minimum density of independent sets in a $K_t$-free $G$ can be used to provide lower bounds for multicolor Ramsey numbers. In…
The purpose of this paper is to introduce the idea of triangular Ramsey numbers and provide values as well as upper and lower bounds for them. To do this, the combinatorial game Mines is introduced; after some necessary theorems about…
A recent breakthrough of Conlon and Ferber yielded an exponential improvement on the lower bounds for multicolor diagonal Ramsey numbers. In this note, we modify their construction and obtain improved bounds for more than three colors.
In this paper we introduce a general framework for proving lower bounds for various Ramsey type problems within random settings. The main idea is to view the problem from an algorithmic perspective: we aim at providing an algorithm that…
We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits.