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 |
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Article number | 101964 |
Pages (from-to) | 1-16 |
Number of pages | 16 |
Journal | Computational Geometry: Theory and Applications |
Volume | 110 |
DOIs | |
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