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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
10.4. BOX-RECTANGULAR DRAWING 337
(c) 2c
2
+c
3
4 for every independent set S of cycles consisting of 2-legged cycles and
3-legged cycles, where c
2
and c
3
are the numbers of 2-legged cycles and 3-legged
cycles in S, respectively.
a
d
G
C
1
C
2
6
C
C
5
c
b
3
C
C
4
Figure 10.22 Plane graph. (Figure taken from [NR04].)
For the set S
1
= {C
1
, C
2
} above c
2
= 2, c
3
= 0 and hence 2c
2
+ c
3
= 4, while for
S
2
= {C
2
, C
3
, C
4
} c
2
= 1 and c
3
= 2 and hence 2c
2
+ c
3
= 4.
It is rather easy to prove the necessity of Theorem 10.4.
In order to prove the sufficiency of Theorem 10.4, it suffices to show that if the three
conditions (a)–(c) in Theorem 10.4 hold then one can choose four outer vertices of degree ...
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Publisher Resources

ISBN: 9781420010268