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GD
2006
Springer
14 years 2 months ago
Computing Geometric Minimum-Dilation Graphs Is NP-Hard
We prove that computing a geometric minimum-dilation graph on a given set of points in the plane, using not more than a given number of edges, is an NP-hard problem, no matter if ...
Rolf Klein, Martin Kutz
COMGEO
2010
ACM
13 years 10 months ago
Mixed volume techniques for embeddings of Laman graphs
We use Bernstein's Theorem [1] to obtain combinatorial bounds for the number of embeddings of Laman graph frameworks modulo rigid motions. For this, we study the mixed volume...
Reinhard Steffens, Thorsten Theobald
COMBINATORICS
2006
107views more  COMBINATORICS 2006»
13 years 10 months ago
The Linear Complexity of a Graph
The linear complexity of a matrix is a measure of the number of additions, subtractions, and scalar multiplications required to multiply that matrix and an arbitrary vector. In th...
David L. Neel, Michael E. Orrison
COMBINATORICS
2006
135views more  COMBINATORICS 2006»
13 years 10 months ago
Drawing a Graph in a Hypercube
A d-dimensional hypercube drawing of a graph represents the vertices by distinct points in {0, 1}d, such that the line-segments representing the edges do not cross. We study lower...
David R. Wood
JCT
2006
70views more  JCT 2006»
13 years 10 months ago
Sparse halves in triangle-free graphs
One of Erdos' favourite conjectures was that any triangle-free graph G on n vertices should contain a set of n/2 vertices that spans at most n2/50 edges. We prove this when t...
Peter Keevash, Benny Sudakov