... endpoint of one of his paths and the electronic journal of combinatorics 16 (2009), #R28 12Following [2], we define τ(Hn) to be the minimum number of moves needed for Maker in order to win Hn(it ... Knwhich is induced on the vertices of Bk(S). LetGk(S) be the subgraph of Gk(S) which is obtained by removing all edges (x, y) such thatx and y are endpoints of the same path of Maker. The ... p1are the endpoints of P and v, ware the neighbors of u in C. In his (k0+ 1)st move, Maker claims the edge (u, p0). Makercan win by claiming either (v, p1) or (w, p1) in his next move....