Bekos, Michael A. and Gronemann, Martin and Kaufmann, Michael and Krug, Robert (2015) Planar Octilinear Drawings with One Bend Per Edge.
Published in: Journal of Graph Algorithms and Applications: Special Issue on Selected Papers from the 22nd International Symposium on Graph Drawing (GD2014). ISSN 1526-1719

Abstract

In octilinear drawings of planar graphs, every edge is drawn as a sequence of horizontal, vertical and diagonal (45°) 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 at most 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(n2) ×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 for some edges.

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