Recognizing and Drawing IC-Planar Graphs

Brandenburg, Franz J. and Didimo, Walter and Evans, William S. and Kindermann, Philipp and Liotta, Giuseppe and Montecchiani, Fabrizio (2015) Recognizing and Drawing IC-Planar Graphs. In: Graph Drawing and Network Visualization: 23rd International Symposium, GD 2015, September 24-26, 2015, Los Angeles, CA, USA , pp. 295-308 (Official URL: http://dx.doi.org/10.1007/978-3-319-27261-0_25).

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Abstract

IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph G with n vertices, we present an O(n)-time algorithm that computes a straight-line drawing of G in quadratic area, and an O(n^3)-time algorithm that computes a straight-line drawing of G with right-angle crossings in exponential area. Both these area requirements are worst-case optimal. We also show that it is NP-complete to test IC-planarity both in the general case and in the case in which a rotation system is fixed for the input graph. Furthermore, we describe a polynomial-time algorithm to test whether a set of matching edges can be added to a triangulated planar graph such that the resulting graph is IC-planar.

Item Type:Conference Paper
Classifications:G Algorithms and Complexity > G.420 Crossings
G Algorithms and Complexity > G.770 Planarity Testing
P Styles > P.540 Planar
P Styles > P.720 Straight-line
ID Code:1497

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