The oriented cycle game
Two players A and C play the following game on a graph G. They orient the edges of G alternately with C playing first until all the edges of G have been oriented. The goal of C is to create at least one oriented cycle, while A wants to avoid this and finish with an acyclic orientation. Among other results we determine the minimal integer m=m(n) such that C has a winning strategy on every graph of order n and size m. We also discuss several generalizations of this game. © 1998 Elsevier Science B.V. All rights reserved.
Bollobás, B., & Szabó, T. (1998). The oriented cycle game. Discrete Mathematics, 186 (1-3), 55-67. https://doi.org/10.1016/S0012-365X(97)00224-0