chromatic number of a graph is the smallest number of colors
needed to color vertices such that no two adjacent vertices share the
same color. It was first
proven that the chromatic number of a graph is at most one plus the
maximum degree of the graph. In
1941, R. L. Brooks proved that if the graph is neither a complete graph
nor an odd cycle, then the upper bound for the chromatic number of the
graph can be reduced to just the maximum degree of the graph.
My project is to resolve conjectures whose statements are similar
to Brooks’ Theorem. The conjectures are generated by Graffiti.pc, a
conjecture making program designed by Dr. Ermelinda DeLaVina.