• Montag, den 10.11.2025, 16:00 Uhr, Raum F 59
  Therese Biedl (University of Waterloo): The unbent-number for nonplanar orthogonal drawings
  Abstract:
  One framework for visualizng a graph (introduced by Hlineny and Masarik in 2023) is to use multiple drawings such that edges of the graph have good properties (such as "no crossing") in at least one drawing.   In 2025, Antic et al. studied this framework in the context of planar orthogonal point-drawings, where they demanded that every edge has no bend in at least one of the drawings.    They showed that at most three drawings are always enough for this, and this is tight for some graphs.   In this talk, we consider the same setup, except that we permit crossings in the drawing.     We show that in this case, two orthogonal drawings always suffice (and this is tight).    This is proved via a detour of partitioning the edges of a graph with maximum degree 4 into two subsets that each form a triangle-free cactus, a result that may be of interest in its own right.    (Joint work with T. Antic, G. Liotta and A. Wolff.)

   

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