On RAC Drawings of Graphs with One Bend per Edge

  • Patrizio AngeliniEmail author
  • Michael A. Bekos
  • Henry Förster
  • Michael Kaufmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11282)


A k-bend right-angle-crossing drawing (or k-bend RAC drawing, for short) of a graph is a polyline drawing where each edge has at most k bends and the angles formed at the crossing points of the edges are \(90^\circ \). Accordingly, a graph that admits a \(k\)-bend RAC drawing is referred to as k-bend right-angle-crossing graph (or k-bend RAC, for short). In this paper, we continue the study of the maximum edge-density of \(1\)-bend RAC graphs. We show that an n-vertex \(1\)-bend RAC graph cannot have more than \(5.5n-O(1)\) edges. We also demonstrate that there exist infinitely many n-vertex \(1\)-bend RAC graphs with exactly \(5n-O(1)\) edges. Our results improve both the previously known best upper bound of \(6.5n-O(1)\) edges and the corresponding lower bound of \(4.5n-O(\sqrt{n})\) edges by Arikushi et al. (Comput. Geom. 45(4), 169–177 (2012)).



This project was supported by DFG grant KA812/18-1.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Patrizio Angelini
    • 1
    Email author
  • Michael A. Bekos
    • 1
  • Henry Förster
    • 1
  • Michael Kaufmann
    • 1
  1. 1.Wilhelm-Schickhard-Institut für Informatik, Universität TübingenTübingenGermany

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