Drawing outerplanar graphs using thirteen edge lengths

Ziv Bakhajian; Ohad Noy Feldheim

doi:10.1016/j.comgeo.2022.101964

Drawing outerplanar graphs using thirteen edge lengths

Ziv Bakhajian, Ohad Noy Feldheim^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

Abstract

We show that every outerplanar graph can be linearly embedded in the plane such that the number of distinct distances between pairs of adjacent vertices is at most thirteen and there is no intersection between the image of a vertex and that of an edge not containing it. This extends the work of Alon and the second author, where only overlap between vertices was disallowed, thus settling a problem posed by Carmi, Dujmović, Morin and Wood.

Original language	American English
Article number	101964
Pages (from-to)	1-16
Number of pages	16
Journal	Computational Geometry: Theory and Applications
Volume	110
DOIs	https://doi.org/10.1016/j.comgeo.2022.101964
State	Published - Mar 2023

Bibliographical note

Funding Information:
We would like to thank an anonymous referee for useful remarks which significantly improved the presentation of our results and their context.

Publisher Copyright:
© 2022 Elsevier B.V.

Keywords

Distance number of a graph
Drawing of a graph
Outerplanar graphs
Planar graphs

Access to Document

10.1016/j.comgeo.2022.101964

Cite this

@article{3a1d2d6f36ec4c7086d17f0b995b4b1b,

title = "Drawing outerplanar graphs using thirteen edge lengths",

abstract = "We show that every outerplanar graph can be linearly embedded in the plane such that the number of distinct distances between pairs of adjacent vertices is at most thirteen and there is no intersection between the image of a vertex and that of an edge not containing it. This extends the work of Alon and the second author, where only overlap between vertices was disallowed, thus settling a problem posed by Carmi, Dujmovi{\'c}, Morin and Wood.",

keywords = "Distance number of a graph, Drawing of a graph, Outerplanar graphs, Planar graphs",

author = "Ziv Bakhajian and Feldheim, {Ohad Noy}",

note = "Funding Information: We would like to thank an anonymous referee for useful remarks which significantly improved the presentation of our results and their context. Publisher Copyright: {\textcopyright} 2022 Elsevier B.V.",

year = "2023",

month = mar,

doi = "10.1016/j.comgeo.2022.101964",

language = "American English",

volume = "110",

pages = "1--16",

journal = "Computational Geometry: Theory and Applications",

issn = "0925-7721",

publisher = "Elsevier",

}

TY - JOUR

T1 - Drawing outerplanar graphs using thirteen edge lengths

AU - Bakhajian, Ziv

AU - Feldheim, Ohad Noy

N1 - Funding Information: We would like to thank an anonymous referee for useful remarks which significantly improved the presentation of our results and their context. Publisher Copyright: © 2022 Elsevier B.V.

PY - 2023/3

Y1 - 2023/3

N2 - We show that every outerplanar graph can be linearly embedded in the plane such that the number of distinct distances between pairs of adjacent vertices is at most thirteen and there is no intersection between the image of a vertex and that of an edge not containing it. This extends the work of Alon and the second author, where only overlap between vertices was disallowed, thus settling a problem posed by Carmi, Dujmović, Morin and Wood.

AB - We show that every outerplanar graph can be linearly embedded in the plane such that the number of distinct distances between pairs of adjacent vertices is at most thirteen and there is no intersection between the image of a vertex and that of an edge not containing it. This extends the work of Alon and the second author, where only overlap between vertices was disallowed, thus settling a problem posed by Carmi, Dujmović, Morin and Wood.

KW - Distance number of a graph

KW - Drawing of a graph

KW - Outerplanar graphs

KW - Planar graphs

UR - http://www.scopus.com/inward/record.url?scp=85145562133&partnerID=8YFLogxK

U2 - 10.1016/j.comgeo.2022.101964

DO - 10.1016/j.comgeo.2022.101964

M3 - Article

AN - SCOPUS:85145562133

SN - 0925-7721

VL - 110

SP - 1

EP - 16

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

M1 - 101964

ER -

Drawing outerplanar graphs using thirteen edge lengths

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this