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Connected Subtraction Games on Subdivided Stars (1807.10468v1)
Published 27 Jul 2018 in math.CO and cs.DM
Abstract: 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.