A linear-time algorithm for four-partitioning four-connected planar graphs
Information Processing Letters
Algorithms for area-efficient orthogonal drawings
Computational Geometry: Theory and Applications - Special issue on geometric representations of graphs
Directional Routing via Generalized st-Numberings
SIAM Journal on Discrete Mathematics
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Regular Edge Labelings and Drawings of Planar Graphs
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Algorithms for computing a parameterized st-orientation
Theoretical Computer Science
Applications of parameterized st-orientations in graph drawing algorithms
GD'05 Proceedings of the 13th international conference on Graph Drawing
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An st-orientation or bipolar orientation of a 2-connected graph G is an orientation of its edges to generate a directed acyclic graph with a single source s and a single sink t. Given a plane graph G and two vertices s and t on the exterior face of G, the problem of finding an optimum st-orientation, i.e., an st-orientation in which the length of the longest st-path is minimized, was first proposed indirectly by Rosenstiehl and Tarjan in [14] and then later directly by He and Kao in [6]. In this paper, we prove that, given a 2-connected plane graph G, two vertices s, t, on the exterior face of G and a positive integer K, the decision problem of whether G has an st-orientation, where the maximum length of an st-path is ≤ K, is NP-Complete. This solves a long standing open problem on the complexity of optimum st-orientations for plane graphs.