Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra...
Transcript of Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra...
![Page 1: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/1.jpg)
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
![Page 2: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/2.jpg)
2 Chapter 7 Planarity A: Lec 8
7.1 PLANAR DRAWINGS; SURFACES
Fig 7.1.1
c 2010 by Jonathan L. Gross
![Page 3: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/3.jpg)
Section 7.1 Planar Drawings; Surfaces 3
Fig 7.1.2
c 2010 by Jonathan L. Gross
![Page 4: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/4.jpg)
4 Chapter 7 Planarity A: Lec 8
Three Basic Surfaces
Fig 7.1.3
c 2010 by Jonathan L. Gross
![Page 5: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/5.jpg)
Section 7.1 Planar Drawings; Surfaces 5
Fig 7.1.4
c 2010 by Jonathan L. Gross
![Page 6: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/6.jpg)
6 Chapter 7 Planarity A: Lec 8
Riemann Stereographic Projection
Fig 7.1.5
c 2010 by Jonathan L. Gross
![Page 7: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/7.jpg)
Section 7.1 Planar Drawings; Surfaces 7
Jordan Separation Property
Fig 7.1.6
c 2010 by Jonathan L. Gross
![Page 8: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/8.jpg)
8 Chapter 7 Planarity A: Lec 8
Fig 7.1.7
c 2010 by Jonathan L. Gross
![Page 9: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/9.jpg)
Section 7.1 Planar Drawings; Surfaces 9
c 2010 by Jonathan L. Gross
![Page 10: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/10.jpg)
10 Chapter 7 Planarity A: Lec 8
Applying JCT to K and K
Fig 7.1.8
c 2010 by Jonathan L. Gross
![Page 11: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/11.jpg)
Section 7.1 Planar Drawings; Surfaces 11
c 2010 by Jonathan L. Gross
![Page 12: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/12.jpg)
12 Chapter 7 Planarity A: Lec 8
Fig 7.1.9
c 2010 by Jonathan L. Gross
![Page 13: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/13.jpg)
Section 7.1 Planar Drawings; Surfaces 13
Fig 7.1.10
c 2010 by Jonathan L. Gross
![Page 14: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/14.jpg)
14 Chapter 7 Planarity A: Lec 8
Fig 7.1.11
c 2010 by Jonathan L. Gross
![Page 15: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/15.jpg)
Section 7.2 Subdivision; Homeomorphism 15
7.2 SUBDIVISION; HOMEOMORPHISM
Fig 7.2.2
Fig 7.2.2
Fig 7.2.3
c 2010 by Jonathan L. Gross
![Page 16: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/16.jpg)
16 Chapter 7 Planarity A: Lec 8
Barycentric Subdivision
Fig 7.2.4
c 2010 by Jonathan L. Gross
![Page 17: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/17.jpg)
Section 7.2 Subdivision; Homeomorphism 17
Fig 7.2.5
c 2010 by Jonathan L. Gross
![Page 18: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/18.jpg)
18 Chapter 7 Planarity A: Lec 8
Graph Homeomorphism
Fig 7.2.6
c 2010 by Jonathan L. Gross
![Page 19: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/19.jpg)
Section 7.2 Subdivision; Homeomorphism 19
c 2010 by Jonathan L. Gross
![Page 20: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/20.jpg)
20 Chapter 7 Planarity A: Lec 8
Subgraph Homeomorphism Problem
Fig 7.2.7
c 2010 by Jonathan L. Gross
![Page 21: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/21.jpg)
Section 7.2 Subdivision; Homeomorphism 21
Fig 7.2.8
c 2010 by Jonathan L. Gross
![Page 22: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/22.jpg)
22 Chapter 7 Planarity A: Lec 8
Fig 7.2.9
c 2010 by Jonathan L. Gross
![Page 23: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/23.jpg)
Section 7.3 Extending Planar Drawings 23
7.3 EXTENDING PLANAR DRAWINGS
c 2010 by Jonathan L. Gross
![Page 24: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/24.jpg)
24 Chapter 7 Planarity A: Lec 8
Planar Extensions of a Planar Subgraph
Fig 7.3.1
c 2010 by Jonathan L. Gross
![Page 25: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/25.jpg)
Section 7.3 Extending Planar Drawings 25
Fig 7.3.2
c 2010 by Jonathan L. Gross
![Page 26: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/26.jpg)
26 Chapter 7 Planarity A: Lec 8
Fig 7.3.3
c 2010 by Jonathan L. Gross
![Page 27: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/27.jpg)
Section 7.3 Extending Planar Drawings 27
Amalgamating Planar Graphs
Fig 7.3.4
c 2010 by Jonathan L. Gross
![Page 28: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/28.jpg)
28 Chapter 7 Planarity A: Lec 8
Fig 7.3.5
Fig 7.3.6
c 2010 by Jonathan L. Gross
![Page 29: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/29.jpg)
Section 7.3 Extending Planar Drawings 29
Fig 7.3.7
c 2010 by Jonathan L. Gross
![Page 30: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/30.jpg)
30 Chapter 7 Planarity A: Lec 8
Fig 7.3.8
c 2010 by Jonathan L. Gross
![Page 31: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/31.jpg)
Section 7.3 Extending Planar Drawings 31
Appendages to a Subgraph
Fig 7.3.9
c 2010 by Jonathan L. Gross
![Page 32: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/32.jpg)
32 Chapter 7 Planarity A: Lec 8
c 2010 by Jonathan L. Gross
![Page 33: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/33.jpg)
Section 7.3 Extending Planar Drawings 33
Overlapping Appendages
Fig 7.3.10
c 2010 by Jonathan L. Gross
![Page 34: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/34.jpg)
34 Chapter 7 Planarity A: Lec 8
c 2010 by Jonathan L. Gross
![Page 35: Chapter 7cs4203/files/GT-Lec8.pdf · 2013. 9. 4. · Chapter 7 Planar ity A: Lec 8 7.1 Planar Dra wings and Some Basic Surfaces 7.2 Subdivision and Homeomorphism 7.3 Extending Planar](https://reader035.fdocuments.us/reader035/viewer/2022081621/61271684ca219925bb76476f/html5/thumbnails/35.jpg)
Section 7.8 Supplementary Exercises 35
7.8 SUPPLEMENTARY EXERCISES
c 2010 by Jonathan L. Gross