Parity and Exploration Games on Infinite Graphs

This paper examines two players’ turn-based perfect-information games played on infinite graphs. Our attention is focused on the classes of games where winning conditions are boolean combinations of the following two conditions: (1) the first one states that an infinite play is won by player 0 if during the play infinitely many different vertices were visited, (2) the second one is the well known parity condition generalized to a countable number of priorities.

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