Learn More
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 their explosive rate of growth. Recently, an algorithm that can be implemented using adiabatic quantum evolution has(More)
A machine consisting of nearly 100 quantum circuit elements can compute the solution to a classic problem in mathematics, but is it a quantum computer? What is a quantum computer? We could say it's a machine that calculates solutions to problems using quantum components. But this definition is incomplete; after all, an abacus is made of quantum elements(More)
Properties of (connected) graphs whose closed or open neighborhood families are Sperner, anti-Sperner, distinct or none of the proceeding have been extensively examined. In this paper we examine 24 properties of the neighborhood family of a graph. We give asymptotic formulas for the number of (connected) labelled graphs for 12 of these properties. For the(More)