Drawing Graphs with Few Arcs
André Schulz
Artikel in Zeitschriften
erschienen in:
Journal of Graph Algorithms and Applications, Vol. 19, no. 1, 2015, pp. 393-412

Let G=(V,E) be a planar graph. An arrangement of circular arcs is called a composite arc-drawing of G, if its 1-skeleton is isomorphic to G. Similarly, a composite segment-drawing is described by an arrangement of straight-line segments. We ask for the smallest possible ground set of arcs/segments for a composite arc/segment-drawing. We present algorithms for constructing composite arc-drawings with a small ground set for trees, series-parallel graphs, planar 3-trees and general planar graphs. In the case where G is a tree, we also introduce an algorithm that realizes the vertices of the composite drawing on a O(n1.81) ×n grid. For each of the graph classes we provide a lower bound for the maximal size of the arrangement's ground set.

Journal Website
@Article{s15, author = {{Andr{\'e} {Schulz}}, title = {Drawing Graphs with Few Arcs}, journal = {Journal of Graph Algorithms and Applications}, year = {2015}, volume = {19}, number = {1}, pages = {393--412}, doi = {10.7155/jgaa.00366} }