Graph Theory, Lecture 11: Planarity II: properties of plane graphs and Euler's formula

Basic properties of plane graphs (from 28:40). Plane vs planar: are maximally plane graphs maximally planar? (Proof of Lemma 4.2.8 omitted; assume Lemma 4.2.6 for a simpler proof.) Surfaces and their classification (35:15). Euler characteristic: an invariant of surfaces. Proof of Euler's formula for graphs (from 44:47). Example of double counting (1:05:30). Covers rest of Chapter 4.2. Based on R.Diestel, Graph Theory, Springer GTM173, 6th edition 2025. Ebooks available at https://diestel-graph-theory.com under links "Standard eBook" and "Professional Edition".