Connected Subtraction Games on Subdivided Stars
Provides theoretical results for a generalization of takeaway games, but the contribution is incremental and domain-specific to combinatorial game theory.
The paper studies connected subtraction games on graphs, deriving general periodicity results and specific outcomes for subdivided stars, showing that the Sprague-Grundy values are periodic.
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.