Topic: Dual Graphs and Map Coloring

Worked Five-Colorings of Plane Graphs

Triangulations and Cubic Duals

Translating Map Coloring into Dual Vertex Coloring

The Low-Degree Vertex Lemma for Planar Graphs

The Four Color Theorem and Its Meaning

Tait’s Reformulation of the Four Color Theorem

Spanning Trees and Cotrees

Reducible Configurations and Unavoidable Sets

Recovering a Plane Graph from Its Dual

Kempe’s Attempt and Heawood’s Correction