Related papers: A Novel Paradigm for Calculating Ramsey Number via…
Using computational techniques we derive six new upper bounds on the classical two-color 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…
This paper proposes an effective method for estimating the parameters of double-cage induction motors by using Artificial Bee Colony (ABC) algorithm. For this purpose the unknown parameters in the electrical model of asynchronous machine…
Artificial Bee Colony (ABC) optimization algorithm is one of the recent population based probabilistic approach developed for global optimization. ABC is simple and has been showed significant improvement over other Nature Inspired…
Using computer algorithms we establish that the Ramsey number $R(3,K_{10}-e)$ is equal to 37, which solves the smallest open case for Ramsey numbers of this type. We also obtain new upper bounds for the cases of $R(3,K_k-e)$ for $11 \le k…
This paper explores the use of the Artificial Bee Colony (ABC) algorithm to compute threshold selection for image segmentation. ABC is a heuristic algorithm motivated by the intelligent behavior of honey-bees which has been successfully…
A new Approximate Bayesian Computation (ABC) algorithm for Bayesian updating of model parameters is proposed in this paper, which combines the ABC principles with the technique of Subset Simulation for efficient rare-event simulation, first…
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,…
The Artificial Bee Colony (ABC) is the name of an optimization algorithm that was inspired by the intelligent behavior of a honey bee swarm. It is widely recognized as a quick, reliable, and efficient methods for solving optimization…
Ramsey theory is a highly active research area in mathematics that studies the emergence of order in large disordered structures. Ramsey numbers mark the threshold at which order first appears and are extremely difficult to calculate due to…
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 $R(m,n)$…
The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers $R(m,n)$ with $m,n\geq 3$, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey…
Artificial Bee Colony (ABC) is a distinguished optimization strategy that can resolve nonlinear and multifaceted problems. It is comparatively a straightforward and modern population based probabilistic approach for comprehensive…
In this article we give the generalized triangle Ramsey numbers R(K3,G) of 12 005 158 of the 12 005 168 graphs of order 10. There are 10 graphs remaining for which we could not determine the Ramsey number. Most likely these graphs need…
We present improved lower bounds for nine classical Ramsey numbers: $\mathbf{R}(3, 13)$ is increased from $60$ to $61$, $\mathbf{R}(3, 18)$ from $99$ to $100$, $\mathbf{R}(4, 13)$ from $138$ to $139$, $\mathbf{R}(4, 14)$ from $147$ to…
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.…
This paper sets out the results of a range of searches for linear and cyclic graph colourings with specific Ramsey properties. The new graphs comprise mainly 'template graphs' which can be used in a construction described by the current…
The Artificial Bee Colony (ABC) algorithm is an evolutionary optimization algorithm based on swarm intelligence and inspired by the honey bees' food search behavior. Since the ABC algorithm has been developed to achieve optimal solutions by…
Finding exact Ramsey numbers is a problem typically restricted to relatively small graphs. The flag algebra method was developed to find asymptotic results for very large graphs, so it seems that the method is not suitable for finding small…
Approximate Bayesian computation (ABC) is a family of computational techniques in Bayesian statistics. These techniques allow to fi t a model to data without relying on the computation of the model likelihood. They instead require to…
Let $R(H_1,H_2)$ denote the Ramsey number for the graphs $H_1, H_2$, and let $J_k$ be $K_k{-}e$. We present algorithms which enumerate all circulant and block-circulant Ramsey graphs for different types of graphs, thereby obtaining several…