论文标题
周期的游戏
The Game of Cycles
论文作者
论文摘要
SU（2020）引入的循环游戏在一个简单的连接平面图上及其有限的单元格进行，并且玩家根据水槽源规则与箭头进行轮流标记边缘，从而使游戏具有拓扑风格。游戏的目的是生成一个循环单元格---一个被箭头包围的单元格，朝一个方向骑自行车 - 或使最后可能的移动。我们分析了各种图表的两人游戏，并确定谁具有获胜策略。我们还建立了游戏的拓扑特性：标有每个边缘的板必须具有一个循环单元。
The Game of Cycles, introduced by Su (2020), is played on a simple connected planar graph together with its bounded cells, and players take turns marking edges with arrows according to a sink-source rule that gives the game a topological flavor. The object of the game is to produce a cycle cell---a cell surrounded by arrows all cycling in one direction---or to make the last possible move. We analyze the two-player game for various classes of graphs and determine who has a winning strategy. We also establish a topological property of the game: that a board with every edge marked must have a cycle cell.
