论文标题
$ k^{\ aleph_0} $ game：顶点着色
The $K^{\aleph_0}$ Game: Vertex Colouring
论文作者
论文摘要
我们在无限完整的图表上调查了制造商和断路器之间玩过的游戏，其顶点带有给定集中的颜色，每种颜色经常出现。玩家交替声称边缘，制造商的目的是声称拥有足够多彩的无限完整子图的所有边缘，而断路器的目的是防止这种情况。我们表明，如果只有有限的颜色有限，那么制造商就能获得一个完整的子图，其中所有颜色经常出现经常出现，但是如果有很多颜色无限多种颜色，则可以防止这种颜色。即使有无限多种颜色，我们也表明制造商可以获得完整的子图，其中无限的许多颜色经常出现。
We investigate games played between Maker and Breaker on an infinite complete graph whose vertices are coloured with colours from a given set, each colour appearing infinitely often. The players alternately claim edges, Makers aim being to claim all edges of a sufficiently colourful infinite complete subgraph and Breakers aim being to prevent this. We show that if there are only finitely many colours then Maker can obtain a complete subgraph in which all colours appear infinitely often, but that Breaker can prevent this if there are infinitely many colours. Even when there are infinitely many colours, we show that Maker can obtain a complete subgraph in which infinitely many of the colours each appear infinitely often.
