2006
After taking a few combinatorics, graph theory, and algorithms courses, I forayed briefly into the world of purely theoretical research. My mentor was Bill Gasarch, Ph.D., a professor of Computer Science* at the University of Maryland.
The general grid k-coloring problem asks: Given an m x n lattice, can you color the vertices (using k colors) in a way such that neither the m x n rectangle nor any m0 x n0 sub-rectangle has monochromatic corners?
I worked on finding bounds for 2-coloring and 3-coloring lattices, like "no grid containing a 5 x 5 sub-grid can be 2-colored." This project is related to Van der Waerden's theorem and, more generally, Ramsey theory.
*: To quote Dr. Gasarch, "I'm a math guy making CS money." His research interests only serve to fortify this statement.
