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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
1.7. VERTEX ADDITION ALGORITHMS 21
the whole graph is obtained. Finally, the following lemma shows that if the process stops,
the graph is not planar.
LEMMA 1.7 Let G be a graph and let ψ be any proper numbering of G. Denote by G
i
,
with i = 1, . . . , n the su bgr aph of G induced by vertices in V
i
= {v | ψ(v) i} and by
B
1
i
, B
2
i
, . . . , B
b
i
i
the b
i
blocks of G
i
. For a given k, 1 k n 1, let Γ(B
j
k
), 1 j b
k
, be
arbitrary embeddings of B
j
k
with the outer vertices of G
k
on their outer faces. If the blocks
of G
k+1
cannot be embedded such that the outer vertices of G
k+1
are on the outer face and
Γ(B
j
k
), 1 j b
k
, are preserved up to a flip, then G is not planar.
Proof: Suppose for a contradiction that G is planar and that there is no planar embedding ...
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Publisher Resources

ISBN: 9781420010268