%0 Journal Article %T An Erd£¿s--Hajnal analogue for permutation classes %A Vincent Vatter %J Mathematics %D 2015 %I arXiv %X Let $\mathcal{C}$ be a permutation class that does not contain all layered permutations or all colayered permutations. We prove that there is a constant $c$ such that every permutation in $\mathcal{C}$ of length $n$ contains a monotone subsequence of length $cn$. %U http://arxiv.org/abs/1511.01076v1