A new lower bound on the maximum number of plane graphs using production matrices

Clemens Huemer; Alexander Pilz; Rodrigo I. Silveira

doi:10.1016/j.comgeo.2019.07.005

A new lower bound on the maximum number of plane graphs using production matrices

Clemens Huemer, Alexander Pilz, Rodrigo I. Silveira^*

^*Corresponding author for this work

Institute of Software Technology (7160)

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

Abstract

We use the concept of production matrices to show that there exist sets of n points in the plane that admit Ω(42.11ⁿ) crossing-free geometric graphs. This improves the previously best known bound of Ω(41.18ⁿ) by Aichholzer et al. (2007).

Original language	English
Pages (from-to)	36-49
Number of pages	14
Journal	Computational Geometry
Volume	84
DOIs	https://doi.org/10.1016/j.comgeo.2019.07.005
Publication status	Published - 1 Nov 2019

Keywords

Graphs counting
Lower bounds
Plane graphs
Production matrix

ASJC Scopus subject areas

Computer Science Applications
Geometry and Topology
Control and Optimization
Computational Theory and Mathematics
Computational Mathematics

Access to Document

10.1016/j.comgeo.2019.07.005

Cite this

@article{9a14306c1c1241859fa13186e706aa78,

title = "A new lower bound on the maximum number of plane graphs using production matrices",

abstract = "We use the concept of production matrices to show that there exist sets of n points in the plane that admit Ω(42.11n) crossing-free geometric graphs. This improves the previously best known bound of Ω(41.18n) by Aichholzer et al. (2007).",

keywords = "Graphs counting, Lower bounds, Plane graphs, Production matrix",

author = "Clemens Huemer and Alexander Pilz and Silveira, {Rodrigo I.}",

year = "2019",

month = nov,

day = "1",

doi = "10.1016/j.comgeo.2019.07.005",

language = "English",

volume = "84",

pages = "36--49",

journal = "Computational Geometry",

issn = "0925-7721",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - A new lower bound on the maximum number of plane graphs using production matrices

AU - Huemer, Clemens

AU - Pilz, Alexander

AU - Silveira, Rodrigo I.

PY - 2019/11/1

Y1 - 2019/11/1

N2 - We use the concept of production matrices to show that there exist sets of n points in the plane that admit Ω(42.11n) crossing-free geometric graphs. This improves the previously best known bound of Ω(41.18n) by Aichholzer et al. (2007).

AB - We use the concept of production matrices to show that there exist sets of n points in the plane that admit Ω(42.11n) crossing-free geometric graphs. This improves the previously best known bound of Ω(41.18n) by Aichholzer et al. (2007).

KW - Graphs counting

KW - Lower bounds

KW - Plane graphs

KW - Production matrix

UR - http://www.scopus.com/inward/record.url?scp=85071354680&partnerID=8YFLogxK

U2 - 10.1016/j.comgeo.2019.07.005

DO - 10.1016/j.comgeo.2019.07.005

M3 - Article

AN - SCOPUS:85071354680

SN - 0925-7721

VL - 84

SP - 36

EP - 49

JO - Computational Geometry

JF - Computational Geometry

ER -

A new lower bound on the maximum number of plane graphs using production matrices

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this