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Published in:
2014 | OriginalPaper | Chapter
Increasing-Chord Graphs On Point Sets
Authors : Hooman Reisi Dehkordi, Fabrizio Frati, Joachim Gudmundsson
Published in: Graph Drawing
Publisher: Springer Berlin Heidelberg
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We tackle the problem of constructing increasing-chord graphs spanning point sets. We prove that, for every point set
P
with
n
points, there exists an increasing-chord planar graph with
O
(
n
) Steiner points spanning
P
. Further, we prove that, for every convex point set
P
with
n
points, there exists an increasing-chord graph with
O
(
n
log
n
) edges (and with no Steiner points) spanning
P
.