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(n3)-time algorithm that computes a straightline 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. Further more, 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.
CITATION STYLE
Brandenburg, F. J., Didimo, W., Evans, W. S., Kindermann, P., Liotta, G., & Montecchiani, F. (2015). Recognizing and drawing IC-planar graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9411, pp. 295–308). Springer Verlag. https://doi.org/10.1007/978-3-319-27261-0_25
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