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No l Grid-Points in Spaces of Small Dimension

  • Hanno Lefmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5034)

Abstract

Motivated by a question raised by Pór and Wood in connection with compact embeddings of graphs in \({\mathbb Z}^d\), we investigate generalizations of the no-three-in-line-problem. For several pairs (k,l) we give algorithmic lower, and upper bounds on the largest sizes of subsets S of grid-points from the d-dimensional T × ⋯ ×T-grid, where no l distinct grid-points of S are contained in a k-dimensional affine or linear subspace.

Keywords

Distinct Point Linear Subspace Small Dimension Collinear Point Independence Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Hanno Lefmann
    • 1
  1. 1.Fakultät für InformatikTU ChemnitzChemnitzGermany

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