Two Trees Which Are Self–intersecting When Drawn Simultaneously
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.
KeywordsPlanar Graph Outer Face Potential Route Outerplanar Graph Graph Drawing
- 2.Duncan, C.A., Eppstein, D., Kobourov, S.G.: The Geometric Thickness of Low Degree Graphs. In: Boissonant, J.-D., Snoeyink, J. (eds.) 23rd Annual Symp. on Computational geometry, pp. 340–346. ACM Press, New York (2004)Google Scholar