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 she receives 1 / 5 less than Bob or better, and this is best possible.
['Daniel Hoske', 'Jonathan Rollin', 'Torsten Ueckerdt', 'Stefan Walzer']
Playing weighted Tron on trees