We introduce the list colouring extension of classical Ramsey numbers. We investigate when the two Ramsey numbers are equal, and in general, how far apart they can be from each other. We find graph sequences where the two are equal and where they are far apart. For $\ell$-uniform cliques we prove that the list Ramsey number is bounded by an exponential function, while it is well-known that the Ramsey number is super-exponential for uniformity at least $3$. This is in great contrast to the graph case where we cannot even decide the question of equality for cliques.

中文翻译：

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列出拉姆齐数字

我们介绍了经典拉姆齐数的列表着色扩展。我们调查两个拉姆齐数何时相等，一般来说，他们可以相距多远。我们找到两者相等且相距较远的图序列。对于 $\ell$-uniform cliques，我们证明列表 Ramsey 数受指数函数的限制，而众所周知，Ramsey 数对于均匀性至少为 $3$ 是超指数的。这与我们甚至无法决定派系平等问题的图情况形成鲜明对比。