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An Erd\H{o}s--Hajnal analogue for permutation classes
Discrete mathematics & theoretical computer science, Permutation Patterns 2015, Tome 18 (2015-2016) no. 2.

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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 $cn$. 
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     author = {Vatter, Vincent},
     title = {An {Erd\H{o}s--Hajnal} analogue for permutation classes},
     journal = {Discrete mathematics & theoretical computer science},
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     number = {2},
     year = {2015-2016},
     doi = {10.46298/dmtcs.1328},
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     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.1328/}
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Vatter, Vincent. An Erd\H{o}s--Hajnal analogue for permutation classes. Discrete mathematics & theoretical computer science, Permutation Patterns 2015, Tome 18 (2015-2016) no. 2. doi : 10.46298/dmtcs.1328. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.1328/

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