Information Processing Letters
Representations of planar graphs
SIAM Journal on Discrete Mathematics
A linear-time algorithm for drawing a planar graph on a grid
Information Processing Letters
Convex drawings of graphs in two and three dimensions (preliminary version)
Proceedings of the twelfth annual symposium on Computational geometry
Circle packings of maps in polynomial time
European Journal of Combinatorics
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Journal of the ACM (JACM)
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
On simultaneous planar graph embeddings
Computational Geometry: Theory and Applications
GD'05 Proceedings of the 13th international conference on Graph Drawing
Two trees which are self–intersecting when drawn simultaneously
GD'05 Proceedings of the 13th international conference on Graph Drawing
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Traditional representations of graphs and their duals suggest the requirement that the dual vertices should be placed inside their corresponding primal faces, and the edges of the dual graph should cross only their corresponding primal edges. We consider the problem of simultaneously embedding a planar graph and its dual on a small integer grid such that the edges are drawn as straight-line segments and the only crossings are between primal-dual pairs of edges. We provide an O(n) time algorithm that simultaneously embeds a 3-connected planar graph and its dual on a (2n - 2) 脳 (2n - 2) integer grid, where n is the total number of vertices in the graph and its dual.