chapter 7cs4203/files/gt-lec8.pdf · 2013. 9. 4. · chapter 7 planar ity a: lec 8 7.1 planar dra...

Chapter 7Planarity A: Lec 8

7.1 Planar Drawings and Some Basic Surfaces7.2 Subdivision and Homeomorphism7.3 Extending Planar Drawings

1 c 2010 by Jonathan L. Gross

2 Chapter 7 Planarity A: Lec 8

7.1 PLANAR DRAWINGS; SURFACES

Fig 7.1.1

c 2010 by Jonathan L. Gross

Section 7.1 Planar Drawings; Surfaces 3

Fig 7.1.2



Three Basic Surfaces

Fig 7.1.3



Fig 7.1.4



Riemann Stereographic Projection

Fig 7.1.5



Jordan Separation Property

Fig 7.1.6



Fig 7.1.7



Applying JCT to K and K

Fig 7.1.8



Fig 7.1.9



Fig 7.1.10



Fig 7.1.11


Section 7.2 Subdivision; Homeomorphism 15

7.2 SUBDIVISION; HOMEOMORPHISM

Fig 7.2.2

Fig 7.2.2

Fig 7.2.3



Barycentric Subdivision

Fig 7.2.4



Fig 7.2.5



Graph Homeomorphism

Fig 7.2.6



Subgraph Homeomorphism Problem

Fig 7.2.7



Fig 7.2.8



Fig 7.2.9


Section 7.3 Extending Planar Drawings 23

7.3 EXTENDING PLANAR DRAWINGS



Planar Extensions of a Planar Subgraph

Fig 7.3.1



Fig 7.3.2



Fig 7.3.3



Amalgamating Planar Graphs

Fig 7.3.4



Fig 7.3.5

Fig 7.3.6



Fig 7.3.7



Fig 7.3.8



Appendages to a Subgraph

Fig 7.3.9



Overlapping Appendages

Fig 7.3.10


Section 7.8 Supplementary Exercises 35

7.8 SUPPLEMENTARY EXERCISES


chapter 7cs4203/files/gt-lec8.pdf · 2013. 9. 4. · chapter 7 planar ity a: lec 8 7.1 planar dra...

Documents