Strictly-Convex Drawings of 3-Connected Planar Graphs

08/29/2022

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by   Michael A. Bekos, et al.

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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) × O(n^2), as shown by Bárány 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) × (5n^3-4n^2).