... prevent it. In the special case G = K3, the following theorem was proved in [4].Theorem 1. If q <√2n + 2 − 5/2, then Maker has a winning strategy for G(K3; n, q).On the other hand, if ... = K3. Our main result is the following strengthening of Theorem 1.Theorem 4. If q ≥ (2 − 1/24)√n, then for almost all n, Breaker has a wi nning s trategyin the game G(K3; n, q).Remark. ... positional games on graphs that have attracted considerableattention include the diameter game [1], the planarity, colorability, and minor games [6].For more information on positional games, we...