Ziv Bakhajian, Ohad N. Feldheim
Published 2019-07-28Version 1
It is shown that every outerplanar graph $G$ could be linearly embedded in the plane so 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 settles a problem of Carmi, Dujmovi\'{c}, Morin and Wood.
Comments: 21 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1208.0744
On distinct distances in homogeneous sets in the Euclidean space
A note on 1-2-3 and 1-2 Conjectures for 3-regular graphs
Spanning trees without adjacent vertices of degree 2
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