1. HV-planarity: Algorithms and complexity.
- Author
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Didimo, Walter, Liotta, Giuseppe, and Patrignani, Maurizio
- Subjects
- *
COMPUTATIONAL complexity , *PLANAR graphs , *PROBLEM solving , *APPROXIMATION algorithms , *COMPUTER algorithms - Abstract
Abstract An HV-graph is a planar graph with vertex-degree at most four such that each edge is labeled either H (horizontal) or V (vertical). The HV-planarity testing problem asks whether an HV-graph admits an HV-drawing , that is, a planar drawing such that each edge with label H is drawn as a horizontal segment and each edge with label V is drawn as a vertical segment. We prove that the HV-planarity testing problem is NP-complete even for graphs with vertex-degree at most three, which answers an open question posed by both Manuch et al. [30] and Durocher et al. [17]. On the positive side, we prove that the HV-planarity testing problem can be solved in polynomial-time for series-parallel graphs. This result significantly extends a previous result by Durocher et al. about HV-planarity testing of biconnected outerplanar graphs of maximum vertex-degree three. Highlights • HV-planarity testing is NP-complete, even for graphs with vertex-degree at most 3. • Polynomial-time HV-planarity testing for 2-connected series-parallel graphs. • Polynomial-time HV-planarity testing for partial 2-trees. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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