The Largest Connected Subgraph Game

This paper introduces the largest connected subgraph game played on an undirected graph G. In each round, Alice first colours uncoloured vertex of G red, and then, Bob blue, with all vertices initially uncoloured. Once are coloured, (Bob, resp.) wins if there is a red (blue, whose order greater than any blue (red, subgraph. We prove that, plays optimally, then can never win, define large class graphs (called reflection graphs) in which draw. show that determining outcome PSPACE-complete, even bipartite small diameter, recognising GI-hard. also draw paths only path or has at least 11 vertices, cycles cycle odd length. Lastly, we give algorithm to determine cographs linear time.