Publications in Scientific Journals:

C. Duncan, D. Eppstein, M.T. Goodrich, S.G. Kobourov, M. Löffler, M. Nöllenburg:
"Planar and poly-arc Lombardi drawings";
Journal of Computational Geometry, 9 (2018), 1; 328 - 355.

English abstract:
In Lombardi drawings of graphs, edges are represented as circular arcs and the edges incident on vertices have perfect angular resolution. It is known that not every planar graph has a planar Lombardi drawing. We give an example of a planar 3-tree that has no planar Lombardi drawing and we show that all outerpaths do have a planar Lombardi drawing. Further, we show that there are graphs that do not even have any Lombardi drawing at all. With this in mind, we generalize the notion of Lombardi drawings to that of (smooth) k-Lombardi drawings, in which each edge may be drawn as a (differentiable) sequence of k circular arcs; we show that every graph has a smooth 2-Lombardi drawing and every planar graph has a smooth planar 3-Lombardi drawing. We further investigate related topics connecting planarity and Lombardi drawings.

"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)

Electronic version of the publication:

Created from the Publication Database of the Vienna University of Technology.