Embedding graphs in books: a layout problem with applications to VLSI design
SIAM Journal on Algebraic and Discrete Methods
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
Stack and Queue Layouts of Directed Acyclic Graphs: Part I
SIAM Journal on Computing
Stack and Queue Layouts of Directed Acyclic Graphs: Part II
SIAM Journal on Computing
The pagenumber of k-trees is O(k)
Discrete Applied Mathematics
Stack and Queue Layouts of Posets
SIAM Journal on Discrete Mathematics
Series-Parallel Planar Ordered Sets Have Pagenumber Two
GD '96 Proceedings of the Symposium on Graph Drawing
On Embedding an Outer-Planar Graph in a Point Set
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
Linkless symmetric drawings of series parallel digraphs
Computational Geometry: Theory and Applications
Curve-constrained drawings of planar graphs
Computational Geometry: Theory and Applications
Graph treewidth and geometric thickness parameters
GD'05 Proceedings of the 13th international conference on Graph Drawing
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An optimal O(n)-time algorithm to compute an upward two-page book embedding of a series-parallel digraph with n vertices is presented. A previous algorithm of Alzohairi and Rival [1] runs in O(n3) time and assumes that the input series-parallel digraph does not have transitive edges. One consequence of our result is that series-parallel (undirected) graphs are necessarily sub-hamiltonian. This extends a previous result by Chung, Leighton, and Rosenberg [5] who proved sub-hamiltonicity for a subset of planar series-parallel graphs. Also, this paper investigates the problem of mapping planar digraphs onto a given set of points in the plane, so that the edges are drawn upward planar. This problem is called the upward point-set embedding problem. The equivalence between the problem of computing an upward two-page book embedding and an upward point-set embedding with at most one bend per edge on any given set of points is proved. An O(n log n)-time algorithm for computing an upward point-set embedding with at most one bend per edge on any given set of points for planar series-parallel digraphs is presented.