3-Monotone Expanders

Bourgain recently constructed $O(1)$-monotone bipartite expanders. By combining this result with a generalisation of the unraveling method of Kannan, we construct 3-monotone bipartite expanders, which is best possible. Similarly, we construct bipartite expanders that have 3-page book embeddings, 2-queue layouts, and 4-track layouts. All these results are best possible.

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