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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
8.3. RESULTS IN THE GENERAL SCENARIO 257
graph. I ns t ead, the sequence of vertices is such that, if du mmy edges are inserted between
non-adjacent vertices that are consecutive in the sequence, then the resulting drawing is
still a k-spine, 1-bend drawing. The following lemma holds.
LEMMA 8.2 If G is a maximal planar graph that is k-spine, 1-ben d drawable for k 2,
then there exists a simple cycle C in G such that G \ C is (k 1)-spine, 1-bend drawable.
(a)
(b)
Figure 8.7 (a) A planar 2-spine, 1-bend drawing of a planar graph G. (b) A cutting cycle
of G. Figure taken from [DD LS 06].
We can use now the neces s ary condition expressed by Lemma 8.2 ...
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Publisher Resources

ISBN: 9781420010268