Two trees which are self–intersecting when drawn simultaneously

Authors:
Markus Geyer;Michael Kaufmann;Imrich Vrťo
Affiliations:
WSI für Informatik, Universität Tübingen, Tübingen, Germany;WSI für Informatik, Universität Tübingen, Tübingen, Germany;Institute of Mathematics, Slovak Academy of Sciences, Bratislava, Slovakia
Venue:
GD'05 Proceedings of the 13th international conference on Graph Drawing
Year:
2005

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Abstract

An actual topic in the graph drawing is the question how to draw two edge sets on the same vertex set, the so-called simultaneous drawing of graphs. The goal is to simultaneously find a nice drawing for both of the sets. It has been found out that only restricted classes of planar graphs can be drawn simultaneously using straight lines and without crossings within the same edge set. In this paper, we negatively answer one of the most often posted open questions namely whether any two trees with the same vertex set can be drawn simultaneously crossing-free in a straight line way.