论文标题
HyperCube在HyperCube上的制造商突破游戏的配对策略与子立方体作为获胜套装
Pairing strategies for the Maker-Breaker game on the hypercube with subcubes as winning sets
论文作者
论文摘要
我们认为在$ n $ dimensional HyperCube $ \ {0,1 \}^n $的顶点上的制造商 - 破坏者位置游戏，其中包括$ k $ - 二维子立方体作为获胜集。我们描述了一种配对策略，如果$ n $是4和$ k \ ge n/4 +1 $的功率，则可以打破破坏者获胜。我们的结果还暗示，对于所有$ n \ geq 3 $，如果$ k \ ge \ weft \ lfloor \ frac {3} {7} {7} n \ right \ rfloor +rfloor +1 $。
We consider the Maker-Breaker positional game on the vertices of the $n$-dimensional hypercube $\{0,1\}^n$ with $k$-dimensional subcubes as winning sets. We describe a pairing strategy which allows Breaker to win if $n$ is a power of 4 and $k \ge n/4 +1$. Our results also imply that for all $n \geq 3$ there is a Breaker's win pairing strategy if $k \ge \left\lfloor\frac{3}{7}n\right\rfloor +1$.
