论文信息 - Strictly Convex Drawings of Planar Graphs

Strictly Convex Drawings of Planar Graphs

Every three-connected planar graph with n vertices has a drawing on an O(n 2 ) × O(n 2 ) grid in which all faces are strictly convex polygons. These drawings are obtained by perturbing (not strictly) convex drawings on O(n) × O(n) grids. Tighter bounds are obtained when the faces have fewer sides. In the proof, we derive an explicit lower bound on the number of primitive vectors in a triangle.

B Imre | B. Imre

[1] M. Chrobak,et al. Convex Grid Drawings of 3-Connected Planar Graphs , 1997, Int. J. Comput. Geom. Appl..

[2] Jürgen Richter-Gebert. Realization Spaces of Polytopes , 1996 .

[3] Jovisa D. Zunic,et al. On the Maximal Number of Edges of Convex Digital Polygons Included into an m x m -Grid , 1995, J. Comb. Theory, Ser. A.

[4] Walter Schnyder,et al. Embedding planar graphs on the grid , 1990, SODA '90.

[5] Stefan Felsner,et al. Geodesic Embeddings and Planar Graphs , 2003, Order.

[6] Stefan Felsner,et al. Convex Drawings of Planar Graphs and the Order Dimension of 3-Polytopes , 2001, Order.

[7] Norihide Tokushige,et al. The Minimum Area of Convex Lattice n-Gons , 2004, Comb..

[8] Günter Rote. Strictly convex drawings of planar graphs , 2005, SODA.

[9] E. Wright,et al. An Introduction to the Theory of Numbers , 1939 .

[10] János Pach,et al. How to draw a planar graph on a grid , 1990, Comb..

[11] W. T. Tutte. Convex Representations of Graphs , 1960 .