Type of Culminating Activity
Master of Science in Mathematics
Andres E. Caicedo, Ph.D.
This thesis considers several coloring problems all of which have a combinatorial flavor. We review some results on the chromatic number of the plane, and improve a bound on the value of regressive Ramsey numbers. The main work of this thesis considers the problem of whether given any n ≥ 1; one can color Z+ in such a way that for all a ϵ Z+ the numbers a, 2a, 3a, ..., na are assigned different colors. Such colorings are referred to as satisfactory. We provide a sufficient condition for guaranteeing the existence of satisfactory colorings and analyze the resulting structure. Explicit constructions are given for n ≤ 54: The thesis concludes with some suggestions towards a general argument.
Chartier, Thomas Antonio Charles, "Coloring Problems" (2011). Boise State University Theses and Dissertations. Paper 231.