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arXiv · 2508.19913

Internally-Convex Drawings of Outerplanar Graphs in Small Area

Michael A. Bekos·Giordano Da Lozzo·Fabrizio Frati·Giuseppe Liotta·Antonios Symvonis
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Abstract

A well-known result by Kant [Algorithmica, 1996] implies that $n$-vertex outerplane graphs admit embedding-preserving planar straight-line grid drawings where the internal faces are convex polygons in $O(n^{2})$ area. In this paper, we present an algorithm to compute such drawings in $O(n^{1.5})$ area. We also consider outerplanar drawings in which the internal faces are required to be strictly-convex polygons. In this setting, we provide a $\Theta(nk^2)$ area bound for $n$-vertex outerplanar graphs whose weak dual is a path and whose maximum face size is $k$ and a $\Theta(nd^2)$ area bound for $n$-vertex outerplanar graphs whose diameter is bounded by $d$.

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Michael A. Bekos, Giordano Da Lozzo, Fabrizio Frati, Giuseppe Liotta, Antonios Symvonis. 2025-08-27. Internally-Convex Drawings of Outerplanar Graphs in Small Area. https://arxiv.org/abs/2508.19913

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