  The present paper deals with connected subtraction games in graphs, which are
generalization of takeaway games. In a connected subtraction game, two players
alternate removing a connected sub-graph from a given connected game-graph,
provided the resulting graph is connected, and provided the number of vertices
of the removed subgraph belongs to a prescribed set of integers. We derive
general periodicity results on such games, as well as specific results when
played on subdivided stars.
