Hoepner, Julia

Project title: Eternal Roman Domination

Department: Mathematics and Statistics

Faculty supervisor: Dr. Gary MacGillivray

"We will define and analyze a combinatorial game that is an eternal extension of Roman domination: the player must guard against an infinite sequence of attacks to maintain a Roman dominating set.  This project will first investigate several variations of the game and draw comparisons to corresponding results for eternal domination.  A basis for further research along those branches will established before focusing on one.  We expect to determine bounds on the number of required guards, criteria for which player has a winning strategy, and a give a precise description of such strategies when the game is played on graphs belonging to well-structured families."