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The Maximum Number of Edges in Geometric Graphs with Pairwise Virtually Avoiding Edges

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Abstract

Let G be a geometric graph on n vertices that are not necessarily in general position. Assume that no line passing through one edge of G meets the relative interior of another edge. We show that in this case the number of edges in G is at most 2n−3.

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Authors and Affiliations

  1. Department of Mathematics, Physics, and Computer Science, University of Haifa at Oranim, Tivon, 36006, Israel

    Eyal Ackerman

  2. Mathematics Department, Technion, Israel Institute of Technology, Haifa, 32000, Israel

    Noa Nitzan & Rom Pinchasi

Authors
  1. Eyal Ackerman
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  2. Noa Nitzan
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  3. Rom Pinchasi
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Correspondence to Noa Nitzan.

Additional information

Supported by ISF grant (Grant No. 1357/12) and by BSF grant (Grant No. 2008290).

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Ackerman, E., Nitzan, N. & Pinchasi, R. The Maximum Number of Edges in Geometric Graphs with Pairwise Virtually Avoiding Edges. Graphs and Combinatorics 30, 1065–1072 (2014). https://doi.org/10.1007/s00373-013-1335-7

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  • DOI: https://doi.org/10.1007/s00373-013-1335-7

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