TY - JOUR
T1 - Drawing outerplanar graphs using three edge lengths
AU - Alon, Noga
AU - Feldheim, Ohad N.
N1 - Publisher Copyright:
©2014 Elsevier B.V. All rights reserved.
PY - 2015/3
Y1 - 2015/3
N2 - 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.
AB - 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.
KW - Degenerate drawing of a graph
KW - Distance number of a graph
KW - Outerplanar graphs
UR - http://www.scopus.com/inward/record.url?scp=84908428979&partnerID=8YFLogxK
U2 - 10.1016/j.comgeo.2014.10.006
DO - 10.1016/j.comgeo.2014.10.006
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AN - SCOPUS:84908428979
SN - 0925-7721
VL - 48
SP - 260
EP - 267
JO - Computational Geometry: Theory and Applications
JF - Computational Geometry: Theory and Applications
IS - 3
ER -