ANALYSIS OF THREE NEW COMBINATORIAL GAMES
Paul Ottaway · 2003
This thesis will present three combinatorial games: Vertex Deletion, Grand Left/Right and Cookie Cutter. Vertex Deletion is a game played on a graph. One version of the game is completely solved while the values of games played on complete graphs, paths, cycles, complete bipartite graphs and stars are examined in others. For a particular version we also demonstrate a decomposition theorem. We introduce the notion of even and odd games and show that it relates to both Vertex Deletion and Grand Left/Right. Cookie cutter is played by removing squares from a grid of a fixed size. We find a relation between this game and a set of octal games. Starting positions with one and two rows are completely solved in one version of the game.