On the light side of geometric graphs

Eyal Ackerman; Rom Pinchasi

doi:10.1016/j.disc.2011.12.009

On the light side of geometric graphs

Eyal Ackerman, Rom Pinchasi

Faculty of Natural Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

Let G be a geometric graph on n vertices in general position in the plane. Suppose that for every line ℓ in the plane the subgraph of G induced by the set of vertices in one of the two half-planes bounded by ℓ has at most k edges (k<1 may be a function of n). Then G has at most O(nk) edges. This bound is best possible.

Original language	English
Pages (from-to)	1213-1217
Number of pages	5
Journal	Discrete Mathematics
Volume	312
Issue number	6
DOIs	https://doi.org/10.1016/j.disc.2011.12.009
State	Published - 28 Mar 2012

Bibliographical note

Funding Information:
We thank anonymous referees for several helpful suggestions for improving the presentation of the paper. The second author was supported by BSF grant (grant No. 2008290 ).

Keywords

Geometric graphs
k-near bipartite

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2011.12.009

Cite this

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abstract = "Let G be a geometric graph on n vertices in general position in the plane. Suppose that for every line ℓ in the plane the subgraph of G induced by the set of vertices in one of the two half-planes bounded by ℓ has at most k edges (k<1 may be a function of n). Then G has at most O(nk) edges. This bound is best possible.",

keywords = "Geometric graphs, k-near bipartite",

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N2 - Let G be a geometric graph on n vertices in general position in the plane. Suppose that for every line ℓ in the plane the subgraph of G induced by the set of vertices in one of the two half-planes bounded by ℓ has at most k edges (k<1 may be a function of n). Then G has at most O(nk) edges. This bound is best possible.

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On the light side of geometric graphs

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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