Honors College Theses

Publication Date



Mathematics (B.S.)

Document Type and Release Option

Thesis (open access)

Faculty Mentor

Colton Magnant


Given a complete graph G, we consider two separate scenarios. First, we consider the minimum number N such that every coloring of G using exactly k colors contains either a rainbow triangle or a monochromatic star on t vertices. This number is known for small cases and generalized for larger cases for a fixed k. Second, we introduce the vertex proper connection number of a graph and provide a relationship to the chromatic number of minimally connected subgraphs. Also a notion of total proper connection is introduced and a question is asked about a possible relationship between the total proper connection number and the vertex and edge proper connection numbers.