The project explores graph theory's star coloring parameter, χs. This is a proper coloring where all paths of four vertices use at least three colors. We find a planar graph with h χs=10=10 on the smallest known number of vertices. We also find bounds on the sum of h χs=10 of a graph and its complement. Additionally, we explore the parameter on permutation graphs, Mycielski graphs, and maximal planar graphs and their duals.

• This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

Creator

• Climis, Timothy M.

Publisher

• Worcester Polytechnic Institute

Identifier

• 06D456M

Advisor

• Christopher, Peter R.

Year

• 2006

Date created

• 2006-01-01

Resource type

• Major Qualifying Project

Major

• Mathematical Sciences

Rights statement

• In Copyright