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arXiv · 2208.13388

Strictly-Convex Drawings of $3$-Connected Planar Graphs

Michael A. Bekos·Martin Gronemann·Fabrizio Montecchiani·Antonios Symvonis
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Abstract

Strictly-convex straight-line drawings of $3$-connected planar graphs in small area form a classical research topic in Graph Drawing. Currently, the best-known area bound for such drawings is $O(n^2) \times O(n^2)$, as shown by B\'{a}r\'{a}ny and Rote by means of a sophisticated technique based on perturbing (non-strictly) convex drawings. Unfortunately, the hidden constants in such area bound are in the $10^4$ order. We present a new and easy-to-implement technique that yields strictly-convex straight-line planar drawings of $3$-connected planar graphs on an integer grid of size $2(n-1) \times (5n^3-4n^2)$.

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Michael A. Bekos, Martin Gronemann, Fabrizio Montecchiani, Antonios Symvonis. 2022-08-29. Strictly-Convex Drawings of $3$-Connected Planar Graphs. https://arxiv.org/abs/2208.13388

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