Our project intended to calculate Ramsey numbers. Even though this may seem like a simple task, the time required to calculate even an R(3,4) with simplistic methods on a home computer can be in terms of hours to days. Therefore more specifically, our project attempted to find algorithms and make use of higher-level programming ideas in order to most efficiently calculate Ramsey numbers in the least amount of time. In the end, the results about how much time we were able to save as a result of implementing new algorithms should be just as important as being able to calculate the numbers themselves.
Our project mentor, David Metzler, Ph.D., recommended that we also try not only to calculate Ramsey numbers, but also to reduce the ranges of unknown Ramsey numbers. For instance, an R(4, 6) is known to be greater than 34, but less than 42. If we found a 34-node graph with no monochromatic subgraphs of neither sizes four nor six, we would have made a significant and new discovery in the mathematical sphere. (A list of stated values and known range for Ramsey numbers is available in Appendix C.)