Impartial Intersection Restriction Games
Melissa A. Huggan · 2015
Intersection restriction games are games played on hypergraphs in which options for a player are restricted based on previous play via some intersection property.This paper focuses on two games within this class: Arc-Kayles and a Triple Packing game.Arc-Kayles is a game where, on their turn, players remove an edge and all adjacent edges from a graph.Together, players are forming a maximal matching.The Triple Packing game is a combinatorial design game where players are choosing triples such that no two triples chosen share a pair.Both games are played under normal play.We give new results for Arc-Kayles played on a special star graph and the wheel graph as well as partial results for the Triple Packing game played on the complete graph.I would also like to thank my examination committee members for their suggestions and thought-provoking questions throughout my thesis defence.