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Handbook of Graph Drawing and Visualization
book

Handbook of Graph Drawing and Visualization

by Roberto Tamassia
August 2013
Intermediate to advanced content levelIntermediate to advanced
862 pages
32h 20m
English
Chapman and Hall/CRC
Content preview from Handbook of Graph Drawing and Visualization
14.2. STRAIGHT-LINE AND POLYLINE GRID DRAWINGS 465
that utn(G
n
)
2n. Theorem 14.5 implies that 2XY utn(G
n
)
2n. Hence the
volume is Ω(n
3/2
) [DLMW05].
This result highlights a substantial difference between 3D grid drawings of undirected
graphs and upward 3D grid drawings of dags, since every (undirected) outerplanar graph
has a 3D grid drawing with linear volume [F LW01]. In th e full version of their paper, Di
Giacomo et a l. [DLMW05] constructed an upward 3D grid drawing of G
n
with O(n
3/2
)
volume. It is unknown whether every n-vertex outerplanar dag has an upward 3D grid
drawing with O(n
3/2
) volume.
The proof that every graph has a 3D grid drawing ...
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Publisher Resources

ISBN: 9781420010268