Chapter 7Planarity B: Lec 9
7.4 Kuratowski’s Theorem7.5 Algebraic Tests for Planarity
1 c 2010 by Jonathan L. Gross
2 Chapter 7 Planarity B: Lec 9
7.4 KURATOWSKI’S THEOREM
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Section 7.4 Kuratowski’s Theorem 3
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4 Chapter 7 Planarity B: Lec 9
Step 1: Min Counterex Is Simple & 3-Conn
c 2010 by Jonathan L. Gross
Section 7.4 Kuratowski’s Theorem 5
Step 2: Three Overlapping Appendages
Fig 7.4.3
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6 Chapter 7 Planarity B: Lec 9
Fig 7.4.3
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Section 7.4 Kuratowski’s Theorem 7
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8 Chapter 7 Planarity B: Lec 9
Step 3: Cycle+Appendages Configuration
Fig 7.4.5
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Section 7.4 Kuratowski’s Theorem 9
Fig 7.4.6
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10 Chapter 7 Planarity B: Lec 9
Fig 7.4.7
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Section 7.4 Kuratowski’s Theorem 11
Fig 7.4.8
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12 Chapter 7 Planarity B: Lec 9
Fig 7.4.9
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Section 7.4 Kuratowski’s Theorem 13
Finding K or K in Small Nonplanar Graphs
Fig 7.4.10
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14 Chapter 7 Planarity B: Lec 9
Fig 7.4.11
Fig 7.4.12
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Section 7.4 Kuratowski’s Theorem 15
Fig 7.4.13
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16 Chapter 7 Planarity B: Lec 9
7.5 ALGEBRAIC PLANARITY TESTS
Fig 7.5.1
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Section 7.5 Algebraic Planarity Tests 17
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18 Chapter 7 Planarity B: Lec 9
Fig 7.5.2
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Section 7.5 Algebraic Planarity Tests 19
Fig 7.5.3
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20 Chapter 7 Planarity B: Lec 9
Face-Size Equation
Fig 7.5.4
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Section 7.5 Algebraic Planarity Tests 21
Edge-Face Inequality
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22 Chapter 7 Planarity B: Lec 9
Euler Polyhedral Equation
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Section 7.5 Algebraic Planarity Tests 23
Fig 7.5.6
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24 Chapter 7 Planarity B: Lec 9
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Section 7.5 Algebraic Planarity Tests 25
Fig 7.5.7
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26 Chapter 7 Planarity B: Lec 9
Poincaré Duality
Fig 7.5.8
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Section 7.5 Algebraic Planarity Tests 27
Fig 7.5.9
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28 Chapter 7 Planarity B: Lec 9
Fig 7.5.10
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Section 7.5 Algebraic Planarity Tests 29
Fig 7.5.11
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30 Chapter 7 Planarity B: Lec 9
Algebraic Proofs of Nonplanarity
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Section 7.5 Algebraic Planarity Tests 31
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32 Chapter 7 Planarity B: Lec 9
Nonplanarity Condition for Bipartite Graphs
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Section 7.5 Algebraic Planarity Tests 33
Nonplanar Subgraphs
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34 Chapter 7 Planarity B: Lec 9
Fig 7.5.12
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Section 7.5 Algebraic Planarity Tests 35
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36 Chapter 7 Planarity B: Lec 9
Fig 7.5.14
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Section 7.8 Supplementary Exercises 37
7.8 SUPPLEMENTARY EXERCISES
c 2010 by Jonathan L. Gross