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arXiv · 2607.06968

Layer-Respecting Linear Graph Layouts

Alvin Chiu·David Eppstein·Michael T. Goodrich·Songyu Liu
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Abstract

We show how to visualize a graph, $G=(V,E)$, as a layered drawing, layer-respecting arc diagram, or layer-respecting linear cylindric drawing with a minimum number of edge crossings, where layer-respecting means that layers appear in order on a single line and vertices are grouped by their layers. Even though this problem is NP-hard for general arc diagrams, we show how to create such diagrams with fixed-parameter tractable linear-time algorithms, where the parameter that allows this is the width of a layered graph. Such a layered graph can be obtained from a breadth-first search (BFS), in which case the width is upper bounded by a graph width parameter called the BFS width.

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Alvin Chiu, David Eppstein, Michael T. Goodrich, Songyu Liu. 2026-07-08. Layer-Respecting Linear Graph Layouts. https://arxiv.org/abs/2607.06968

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