Embedding planar graphs in four pages
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
SIAM Journal on Computing
A Linear Time Implementation of SPQR-Trees
GD '00 Proceedings of the 8th International Symposium on Graph Drawing
Drawing Planar Partitions II: HH-Drawings
WG '98 Proceedings of the 24th International Workshop on Graph-Theoretic Concepts in Computer Science
Planarity for Clustered Graphs
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
Degree constrained book embeddings
Journal of Algorithms
On the pagenumber of planar graphs
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
On the page number of upward planar directed acyclic graphs
GD'11 Proceedings of the 19th international conference on Graph Drawing
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In a book embedding the vertices of a graph are placed on the "spine" of a "book" and the edges are assigned to "pages" so that edges on the same page do not cross. In the Partitioned 2-page Book Embedding problem egdes are partitioned into two sets E1 and E2, the pages are two, the edges of E1 are assigned to page 1, and the edges of E2 are assigned to page 2. The problem consists of checking if an ordering of the vertices exists along the spine so that the edges of each page do not cross. Hong and Nagamochi [13] give an interesting and complex linear time algorithm for tackling Partitioned 2-page Book Embedding based on SPQR-trees. We show an efficient implementation of this algorithm and show its effectiveness by performing a number of experimental tests. Because of the relationships [13] between Partitioned 2-page Book Embedding and clustered planarity we yield as a side effect an implementation of a clustered planarity testing where the graph has exactly two clusters.