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

Eyal Ackerman; Noa Nitzan; Rom Pinchasi

doi:10.1007/s00373-013-1335-7

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

Eyal Ackerman, Noa Nitzan, Rom Pinchasi

University of Haifa, Technion - Israel Institute of Technology

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

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.

Original language	American English
Pages (from-to)	1065-1072
Number of pages	8
Journal	Graphs and Combinatorics
Volume	30
Issue number	5
DOIs	https://doi.org/10.1007/s00373-013-1335-7
State	Published - Sep 2014

Keywords

Avoiding edges
Discharging method
Geometric graph
Parallel edges

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1007/s00373-013-1335-7

Cite this

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title = "The Maximum Number of Edges in Geometric Graphs with Pairwise Virtually Avoiding Edges",

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.",

keywords = "Avoiding edges, Discharging method, Geometric graph, Parallel edges",

author = "Eyal Ackerman and Noa Nitzan and Rom Pinchasi",

note = "Funding Information: Supported by ISF grant (Grant No. 1357/12) and by BSF grant (Grant No. 2008290).",

year = "2014",

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doi = "10.1007/s00373-013-1335-7",

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AU - Ackerman, Eyal

AU - Nitzan, Noa

AU - Pinchasi, Rom

N1 - Funding Information: Supported by ISF grant (Grant No. 1357/12) and by BSF grant (Grant No. 2008290).

PY - 2014/9

Y1 - 2014/9

N2 - 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.

AB - 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.

KW - Avoiding edges

KW - Discharging method

KW - Geometric graph

KW - Parallel edges

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U2 - 10.1007/s00373-013-1335-7

DO - 10.1007/s00373-013-1335-7

M3 - Article

SN - 0911-0119

VL - 30

SP - 1065

EP - 1072

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

IS - 5

ER -

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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