  The game subset take-away begins with a simplicial complex \Delta. Two
players take turns removing any element of \Delta as well as all other elements
which contain it, and the last player able to move wins. Graph Chomp is a
special case of subset take-away played on a simplicial complex with only
vertices and edges. The game has previously only been analyzed for complete
graphs, forest graphs, and very small special cases of higher-dimensional
simplicial complexes. We generalize a common method of reducing some game
positions to simpler ones by symmetry and provide a complete analysis of
complete n-partite graphs for arbitrary n and all bipartite graphs. Finally, we
give partial results for odd-cycle pseudotrees, which are non-bipartite graphs
with a single cycle.
