A note on light geometric graphs

Eyal Ackerman; Jacob Fox; Rom Pinchasi

doi:10.1016/j.disc.2013.03.001

A note on light geometric graphs

Eyal Ackerman
, Jacob Fox
, 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. We say that G is k-light if no edge e of G has the property that each of the two open half-planes bounded by the line through e contains more than k edges of G. We extend the previous result in Ackerman and Pinchasi (2012) [1] and with a shorter argument show that every k-light geometric graph on n vertices has at most O(nk) edges. This bound is best possible.

Original language	English
Pages (from-to)	1281-1283
Number of pages	3
Journal	Discrete Mathematics
Volume	313
Issue number	12
DOIs	https://doi.org/10.1016/j.disc.2013.03.001
State	Published - 2013

Bibliographical note

Funding Information:
The second author’s research was supported by a Simons Fellowship, NSF grant DMS-1069197 , and by an MIT NEC Corporation Award. The third author was supported by the ISF grant (grant No. 1357/12 ) and by the 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.2013.03.001

Cite this

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title = "A note on light geometric graphs",

abstract = "Let G be a geometric graph on n vertices in general position in the plane. We say that G is k-light if no edge e of G has the property that each of the two open half-planes bounded by the line through e contains more than k edges of G. We extend the previous result in Ackerman and Pinchasi (2012) [1] and with a shorter argument show that every k-light geometric graph on n vertices has at most O(nk) edges. This bound is best possible.",

keywords = "Geometric graphs k-near bipartite",

author = "Eyal Ackerman and Jacob Fox and Rom Pinchasi",

note = "Funding Information: The second author{\textquoteright}s research was supported by a Simons Fellowship, NSF grant DMS-1069197 , and by an MIT NEC Corporation Award. The third author was supported by the ISF grant (grant No. 1357/12 ) and by the BSF grant (grant No. 2008290 ).",

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doi = "10.1016/j.disc.2013.03.001",

language = "English",

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journal = "Discrete Mathematics",

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AU - Ackerman, Eyal

AU - Fox, Jacob

AU - Pinchasi, Rom

N1 - Funding Information: The second author’s research was supported by a Simons Fellowship, NSF grant DMS-1069197 , and by an MIT NEC Corporation Award. The third author was supported by the ISF grant (grant No. 1357/12 ) and by the BSF grant (grant No. 2008290 ).

PY - 2013

Y1 - 2013

N2 - Let G be a geometric graph on n vertices in general position in the plane. We say that G is k-light if no edge e of G has the property that each of the two open half-planes bounded by the line through e contains more than k edges of G. We extend the previous result in Ackerman and Pinchasi (2012) [1] and with a shorter argument show that every k-light geometric graph on n vertices has at most O(nk) edges. This bound is best possible.

AB - Let G be a geometric graph on n vertices in general position in the plane. We say that G is k-light if no edge e of G has the property that each of the two open half-planes bounded by the line through e contains more than k edges of G. We extend the previous result in Ackerman and Pinchasi (2012) [1] and with a shorter argument show that every k-light geometric graph on n vertices has at most O(nk) edges. This bound is best possible.

KW - Geometric graphs k-near bipartite

UR - https://www.scopus.com/pages/publications/84875446412

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DO - 10.1016/j.disc.2013.03.001

M3 - Article

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SP - 1281

EP - 1283

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 12

ER -

A note on light geometric graphs

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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