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

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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	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

Keywords

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

All Science Journal Classification (ASJC) codes

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

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10.1016/j.comgeo.2022.101964

Cite this

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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",

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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.

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KW - Drawing of a graph

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ER -

Drawing outerplanar graphs using thirteen edge lengths

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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