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Drawing Subcubic 1-Planar Graphs with Few Bends, Few Slopes, and - PowerPoint PPT Presentation

Feb 04, 2023 •173 likes •1.63k views

Drawing Subcubic 1-Planar Graphs with Few Bends, Few Slopes, and Large Angles Philipp Kindermann Cheriton School of Computer Science University of Waterloo Joint work with Fabrizio Montecchiani, Lena Schlipf, and Andr e Schulz Slope

  1. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 v 2 v 1 V 2 : real vertex v 1 v 2

  2. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 v 2 v 1 V 2 : real vertex v 1 v 2

  3. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 v 2 v 1 V 2 : real vertex dummy vertex v 1 v 2

  4. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 v 2 v 1 V 2 : real vertex dummy vertex v 1 v 2 v 1 v 2

  5. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 v 2 v 1 V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 2

  6. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 v 2 v 1 V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2

  7. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 v 2 v 1 V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  8. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 v 2 v 1 V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  9. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 v 2 v 1 V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  10. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 v 2 v 1 V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  11. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 v 2 v 1 V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  12. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 v 2 v 1 V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  13. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 v 2 v 1 V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  14. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 v 2 v 1 V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  15. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 v 2 v 1 V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  16. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 v 2 v 1 V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  17. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 v 2 v 1 V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  18. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  19. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  20. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  21. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  22. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  23. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  24. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  25. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  26. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  27. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  28. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  29. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  30. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  31. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  32. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  33. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  34. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

  35. Cubic 3-Connected ⇒ 1 Bend, 4 Slopes V 2 : real vertex dummy vertex chain v 1 v 2 v 1 v 1 v 2 v 2 V i :

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