1-Bend RAC Drawings of 1-Planar Graphs

Didimo, Walter and Liotta, Giuseppe and Mehrabi, Saeed and Montecchiani, Fabrizio (2016) 1-Bend RAC Drawings of 1-Planar Graphs. In: Graph Drawing and Network Visualization. GD 2016, September, 19. - 21., 2016 , pp. 335-343(Official URL: http://dx.doi.org/10.1007/978-3-319-50106-2_26).

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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 [22]. Also, straight-line RAC drawings always exist for IC-planar graphs [9], 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.

Item Type:	Conference Paper
Classifications:	G Algorithms and Complexity > G.420 Crossings G Algorithms and Complexity > G.560 Geometry P Styles > P.720 Straight-line
URI:	http://gdea.informatik.uni-koeln.de/id/eprint/1553

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