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Octal games are a well-defined family of two-player games played on heaps ofcounters, in which the players remove alternately a certain number of countersfrom a heap, sometimes being allowed to split a heap into two nonempty heaps,until no counter can be removed anymore. We extend the definition of octalgames to play them on graphs: heaps are replaced by connected components andcounters by vertices. Thus, an octal game on a path P\_n is equivalent toplaying the same octal game on a heap of n counters. We study one of thesimplest octal games, called 0.33, in which the players can remove one vertexor two adjacent vertices without disconnecting the graph. We study this game ontrees and give a complete resolution of this game on subdivided stars andbistars.

Octal Games on Graphs: The game 0.33 on subdivided stars and bistars