# 1-Bend RAC Drawings of 1-Planar Graphs

• Walter Didimo
• Giuseppe Liotta
• Saeed Mehrabi
• Fabrizio Montecchiani
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9801)

## 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.

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© Springer International Publishing AG 2016

## Authors and Affiliations

• Walter Didimo
• 1
• Giuseppe Liotta
• 1
• Saeed Mehrabi
• 2
• Fabrizio Montecchiani
• 1
Email author
1. 1.Dipartimento di IngegneriaUniversità degli Studi di PerugiaPerugiaItaly
2. 2.David R. Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada