I was reading this to try to understand how to calculate grundy numbers for cyclic games. However I don't get why there are some infinite positions where the first player wins.
Also to implement the algorithm, would I need a boolean matrix M[v][x] to know whether a vertex (v) has a son which a grundy number value equal to some number (x) ? or is it possible to use less memory (this would be about O(V^2) for V states considering we can get values up to V - 1) ?