Chapter 4 Ramsey Theory – An Introduction
Project by: Nicole Cossey, Naiyuan Guo, Biying Xu, Zen So, and Christine Yang.
\(\textbf{Summary:}\) Our video includes an animation of the pigeonhole principle where \(n\) pigeons are trying to sit in \(k\) pigeonholes \(n \gt k\text{.}\)
The other animation is the \(R (3, 3) = 6\) proof. This is equivalent to six people at a dinner party where it is guaranteed to either have three strangers or three mutual acquaintances. So at each vertex on the complete \(K_6\) graph one person will sit, and the edges connecting the dinner guests will be red if those two people are strangers and blue if they are acquaintances. The animation takes you through the steps of the proof that shows you will always either end up with a blue triangle or a red triangle. These monochromatic triangles represent the three strangers or three mutual acquaintances.