Abstract
We consider the weighted version of the Tron game on graphs where two players, Alice and Bob, each build their own path by claiming one vertex at a time, starting with Alice. The vertices carry non-negative weights that sum up to 1 and either player tries to claim a path with larger total weight than the opponent. We show that if the graph is a tree then Alice can always ensure to get at most 1/5 less than Bob, and that there exist trees where Bob can ensure to get at least 1/5 more than Alice.
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