English

1-Bend RAC Drawings of 1-Planar Graphs

Computational Geometry 2016-08-31 v1

Abstract

A graph is 1-planar if it has a drawing where each edge is crossed at most once. A drawing is RAC (Right Angle Crossing) if the edges cross only at right angles. The relationships between 1-planar graphs and RAC drawings have been partially studied in the literature. It is known that there are both 1-planar graphs that are not straight-line RAC drawable and graphs that have a straight-line RAC drawing but that are not 1-planar. Also, straight-line RAC drawings always exist for IC-planar graphs, a subclass of 1-planar graphs. One of the main questions still open is whether every 1-planar graph has a RAC drawing with at most one bend per edge. We positively answer this question.

Keywords

Cite

@article{arxiv.1608.08418,
  title  = {1-Bend RAC Drawings of 1-Planar Graphs},
  author = {Walter Didimo and Giuseppe Liotta and Saeed Mehrabi and Fabrizio Montecchiani},
  journal= {arXiv preprint arXiv:1608.08418},
  year   = {2016}
}

Comments

Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016)