Abstract:Planar graphs can be represented as intersection graphs of different types of geometric objects in the plane, e.g., circles (Koebe, 1936), line segments (Chalopin & Gonc ¸alves, 2009), L-shapes (Gonc ¸alves et al., 2018). Furthermore, these representations can be obtained in polynomial time when the planar graph is provided as input. For general graphs, however, even deciding whether such representations exist is often NP-hard. We consider apex graphs, i.e., graphs that can be made planar by removing one verte… Show more
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