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- W2891998810 abstract "We present a new model for hybrid planarity that relaxes existing hybrid representations. A graph (G = (V,E)) is (k, p)-planar if V can be partitioned into clusters of size at most k such that G admits a drawing where: (i) each cluster is associated with a closed, bounded planar region, called a cluster region; (ii) cluster regions are pairwise disjoint, (iii) each vertex (v in V) is identified with at most p distinct points, called ports, on the boundary of its cluster region; (iv) each inter-cluster edge ((u,v) in E) is identified with a Jordan arc connecting a port of u to a port of v; (v) inter-cluster edges do not cross or intersect cluster regions except at their endpoints. We first tightly bound the number of edges in a (k, p)-planar graph with (p<k). We then prove that (4, 1)-planarity testing and (2, 2)-planarity testing are NP-complete problems. Finally, we prove that neither the class of (2, 2)-planar graphs nor the class of 1-planar graphs contains the other, indicating that the (k, p)-planar graphs are a large and novel class." @default.
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- W2891998810 date "2018-12-21" @default.
- W2891998810 modified "2023-09-25" @default.
- W2891998810 title "(k, p)-Planarity: A Relaxation of Hybrid Planarity" @default.
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- W2891998810 doi "https://doi.org/10.1007/978-3-030-10564-8_12" @default.
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