Abstract
It is shown that for any outerplanar graph G there is a one to one mapping of the vertices of G to the plane, so that the number of distinct distances between pairs of connected vertices is at most three. This settles a problem of Carmi, Dujmović, Morin and Wood. The proof combines (elementary) geometric, combinatorial, algebraic and probabilistic arguments.
Original language | English |
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Pages (from-to) | 260-267 |
Number of pages | 8 |
Journal | Computational Geometry: Theory and Applications |
Volume | 48 |
Issue number | 3 |
DOIs | |
State | Published - Mar 2015 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:©2014 Elsevier B.V. All rights reserved.
Keywords
- Degenerate drawing of a graph
- Distance number of a graph
- Outerplanar graphs