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arXiv · 2508.19935

Visualizing Treewidth

Alvin Chiu·Thomas Depian·David Eppstein·Michael T. Goodrich·Martin Nöllenburg
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Abstract

A witness drawing of a graph is a visualization that clearly shows a given property of a graph. We study and implement various drawing paradigms for witness drawings to clearly show that graphs have bounded pathwidth or treewidth. Our approach draws the tree decomposition or path decomposition as a tree of bags, with induced subgraphs shown in each bag, and with ''tracks'' for each vertex of the graph connecting its copies in multiple bags. Within bags, we optimize the vertex layout to avoid crossings of edges and tracks. We implement a visualization prototype for crossing minimization using dynamic programming for graphs of small width and heuristic approaches for graphs of larger width. We explore the design space for width-witness drawings and investigate drawing styles that render the subgraph for each bag as an arc diagram with one or two pages or as a circular layout with straight-line edges, and we render tracks either with straight lines or with orbital-radial paths. Finally, we report results from an expert evaluation assessing different witness drawing styles.

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Alvin Chiu, Thomas Depian, David Eppstein, Michael T. Goodrich, Martin Nöllenburg. 2025-08-27. Visualizing Treewidth. https://doi.org/10.7155/jgaa.v30i2.3273

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