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ISAAC
2005
Springer
135views Algorithms» more  ISAAC 2005»
15 years 3 months ago
Embedding Point Sets into Plane Graphs of Small Dilation
Let S be a set of points in the plane. What is the minimum possible dilation of all plane graphs that contain S? Even for a set S as simple as five points evenly placed on the ci...
Annette Ebbers-Baumann, Ansgar Grüne, Marek K...
GD
2004
Springer
15 years 3 months ago
Intersection Reverse Sequences and Geometric Applications
Pinchasi and Radoiˇci´c [11] used the following observation to bound the number of edges of a topological graph without a self-crossing cycle of length 4: if we make a list of t...
Adam Marcus, Gábor Tardos
COMPGEOM
2008
ACM
14 years 12 months ago
Polychromatic colorings of plane graphs
We show that the vertices of any plane graph in which every face is of length at least g can be colored by (3g - 5)/4 colors so that every color appears in every face. This is nea...
Noga Alon, Robert Berke, Kevin Buchin, Maike Buchi...
CORR
2008
Springer
95views Education» more  CORR 2008»
14 years 10 months ago
The Plane-Width of Graphs
Map vertices of a graph to (not necessarily distinct) points of the plane so that two adjacent vertices are mapped at least a unit distance apart. The plane-width of a graph is th...
Marcin Kaminski, Paul Medvedev, Martin Milanic
COMPGEOM
2006
ACM
15 years 4 months ago
Plane embeddings of planar graph metrics
Embedding metrics into constant-dimensional geometric spaces, such as the Euclidean plane, is relatively poorly understood. Motivated by applications in visualization, ad-hoc netw...
MohammadHossein Bateni, Mohammad Taghi Hajiaghayi,...