Characterization and recognition of partial 3-trees
SIAM Journal on Algebraic and Discrete Methods
Combinatorial algorithms for integrated circuit layout
Combinatorial algorithms for integrated circuit layout
Algorithms finding tree-decompositions of graphs
Journal of Algorithms
Laying out graphs using queues
SIAM Journal on Computing
On Linear Recognition of Tree-Width at Most Four
SIAM Journal on Discrete Mathematics
Drawing graphs: methods and models
Drawing graphs: methods and models
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
Drawing Graphs on Two and Three Lines
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
On the Parameterized Complexity of Layered Graph Drawing
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Nice Drawings for Planar Bipartite Graphs
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
Upward drawings of trees on the minimum number of layers
WALCOM'08 Proceedings of the 2nd international conference on Algorithms and computation
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A graph is proper k-layer planar, for an integer k≥ 0, if it admits a planar drawing in which the vertices are drawn on k horizontal lines called layers and each edge is drawn as a straight-line segment between end-vertices on adjacent layers. In this paper, we point out errors in an algorithm of Fößmeier and Kaufmann (CIAC, 1997) for recognizing proper 3-layer planar graphs, and then present a new characterization of this set of graphs that is partially based on their algorithm. Using the characterization, we then derive corresponding linear-time algorithms for recognizing and drawing proper 3-layer planar graphs. On the basis of our results, we predict that the approach of Fößmeier and Kaufmann will not easily generalize for drawings on four or more layers and suggest another possible approach along with some of the reasons why it may be more successful.