This question is from Problem Solving Strategies by Engel, Chapter 4 question 50.
If $K_{14}$ is colored with two colors, there will be a monochromatic quadrangle.
Here, $K_{14}$ is the complete graph with 14 vertices, a coloring means to assign each edge a color (lets say either red or blue) and I am assuming quadrangle means a cycle of length 4.
I know the technique to prove that $R(3,3) = 6$ (the Ramsey number), and I tried to apply it but with no success. For example, if I have a red path of length 3, then I can force the last edge to be blue. I also started by considering that each vertex has 13 neighbors, so each vertex has either more red or blue edges. So there exists at least 7 vertices, each with at least 7 edges of the same color. But I don't see a way to proceed.