We show that anagram-free vertex colouring a $2\times n$ square grid requires a number of colours that increases with $n$. This answers an open question in Wilson's thesis and shows that even graphs of pathwidth $2$ do not have anagram-free colourings with a bounded number of colours.
翻译:我们显示,在2美元乘以n$方格的无方格顶点上,无方格的无方格顶点颜色需要一些以美元增加的颜色。 这回答了威尔逊论文中的一个未决问题, 并表明,即使是路径线图2美元, 也没有含有一定数量颜色的无方格颜色。