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arXiv · 1408.5920

Planar Octilinear Drawings with One Bend Per Edge

Michael A. Bekos·Martin Gronemann·Michael Kaufmann·Robert Krug
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Abstract

In octilinear drawings of planar graphs, every edge is drawn as an alternating sequence of horizontal, vertical and diagonal ($45^\circ$) line-segments. In this paper, we study octilinear drawings of low edge complexity, i.e., with few bends per edge. A $k$-planar graph is a planar graph in which each vertex has degree less or equal to $k$. In particular, we prove that every 4-planar graph admits a planar octilinear drawing with at most one bend per edge on an integer grid of size $O(n^2) \times O(n)$. For 5-planar graphs, we prove that one bend per edge still suffices in order to construct planar octilinear drawings, but in super-polynomial area. However, for 6-planar graphs we give a class of graphs whose planar octilinear drawings require at least two bends per edge.

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Michael A. Bekos, Martin Gronemann, Michael Kaufmann, Robert Krug. 2014-08-25. Planar Octilinear Drawings with One Bend Per Edge. https://arxiv.org/abs/1408.5920

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