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Full-Text Articles in Mathematics
Coloring Problems, Thomas Antonio Charles Chartier
Coloring Problems, Thomas Antonio Charles Chartier
Boise State University Theses and Dissertations
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 …
Combinatorics And Topology Of Curves And Knots, Bailey Ann Ross
Combinatorics And Topology Of Curves And Knots, Bailey Ann Ross
Boise State University Theses and Dissertations
The genus of a graph is the minimal genus of a surface into which the graph can be embedded. Four regular graphs play an important role in low dimensional topology since they arise from curves and virtual knot diagrams. Curves and virtual knots can be encoded combinatorially by certain signed words, called Gauss codes and Gauss paragraphs. The purpose of this thesis is to investigate the genus problem for these combinatorial objects: Given a Gauss word or Gauss paragraph, what is the genus of the curve or virtual knot it represents?