Outside-Obstacle Representations with All Vertices on the Outer Face
Abstract
An obstacle representation of a graph consists of a set of polygonal obstacles and a drawing of as a visibility graph with respect to the obstacles: vertices are mapped to points and edges to straight-line segments such that each edge avoids all obstacles whereas each non-edge intersects at least one obstacle. Obstacle representations have been investigated quite intensely over the last few years. Here we focus on outside-obstacle representations (OORs) that use only one obstacle in the outer face of the drawing. It is known that every outerplanar graph admits such a representation. We strengthen this result by showing that every (partial) 2-tree has an OOR. We also consider restricted versions of OORs where the vertices of the graph form a convex polygon or even a regular polygon. We characterize when the complement of a tree and when a complete graph minus a simple cycle admits a convex OOR. We construct regular OORs for all (partial) outerpaths, cactus graphs, and grids.
Cite
@article{arxiv.2202.13015,
title = {Outside-Obstacle Representations with All Vertices on the Outer Face},
author = {Oksana Firman and Philipp Kindermann and Jonathan Klawitter and Boris Klemz and Felix Klesen and Alexander Wolff},
journal= {arXiv preprint arXiv:2202.13015},
year = {2025}
}
Comments
Has appeared in the Proceedings of the 30th International Symposium on Graph Drawing and Network Visualization (GD 2022)