Layouts of Expander Graphs

TL;DR

This paper constructs optimal 3-monotone bipartite expanders and demonstrates their optimal embedding and layout properties, advancing understanding of graph layouts and expanders.

Contribution

It introduces the first 3-monotone bipartite expanders and proves their optimality in various graph layout parameters.

Findings

Existence of 3-monotone bipartite expanders with optimal properties

Graphs admit 3-page book embeddings, 2-queue layouts, 4-track layouts, and thickness 2

All results are proven to be optimal

Abstract

Bourgain and Yehudayoff 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. We then show that the same graphs admit 3-page book embeddings, 2-queue layouts, 4-track layouts, and have simple thickness 2. All these results are best possible.