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Graph Theory, Lecture 31: Algebraic planarity criteria, and duality of graphs
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Recap of Tutte's generating theorem (3.2.6). Find properties of face boundaries that might characterise planarity.
Sanity check for proof strategies: make sure that what you try to prove on the way follows from what you're aiming for, ie, is not too strong to be true (7:55-9:30).
MacLane's and Tutte's algebraic planarity criteria (4.5.1 and 4.5.2), with slow proofs.
Algebraic duality (from 28:30). Plane duality (from 47:22). Plane duals are abstract duals (from 1:19:45).
Whitney's theorem (1:24:35)
Covers Chapter 4.5-6.
Sanity check for proof strategies: make sure that what you try to prove on the way follows from what you're aiming for, ie, is not too strong to be true (7:55-9:30).
MacLane's and Tutte's algebraic planarity criteria (4.5.1 and 4.5.2), with slow proofs.
Algebraic duality (from 28:30). Plane duality (from 47:22). Plane duals are abstract duals (from 1:19:45).
Whitney's theorem (1:24:35)
Covers Chapter 4.5-6.
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