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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
16 CHAPTER 1. PLANARITY TESTING AND EMBEDDING
all return edges of e
2
ending strictly higher than lowpt(e
1
) belong to t he other
class.
Intuitively, the partition of the back edges into classes L and R corr e sponds to orienting
the fundamental cycles in such a way that those closed by back edges in L are counterclock-
wise while those closed by back edges in R ar e clockwise.
Theorem 1.2 A graph is planar if and only if it admits an LR partition.
Necessity of the condition of Theorem 1.2 is straightforward: given a DFS tree and a
planar embedding of the graph it suffices to assign each back edge to the classes L or
R, depending on whether the fundamental cycle it closes is counterclockwise or clockwise,
respectively. Sufficiency is shown by constructing ...
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Publisher Resources

ISBN: 9781420010268