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.
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Lefmann, H. (2008). No l Grid-Points in Spaces of Small Dimension . In: Fleischer, R., Xu, J. (eds) Algorithmic Aspects in Information and Management. AAIM 2008. Lecture Notes in Computer Science, vol 5034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68880-8_25
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DOI: https://doi.org/10.1007/978-3-540-68880-8_25
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