Some four-color proofs and failures!

These might make sense to you if you're familiar with four-color-theorem proofs; I don't lay out the arguments here. These pages each examine whether a certain subgraph of a minimal counterexample is reducible.

Single node of degree 4

Single node of degree 5

Birkhoff diamond

Wilson, exercise 10.3

Wilson, exercise 10.4

(Wilson is Wilson, Robert A., Graphs, Colourings and the Four-colour Theorem, 2002)

See this project on GitHub.

Sincerely, Izzy Dupree, Elias Zeidan and Sam Auciello.