Topic: Dual Graphs and Map Coloring

Kempe Chains and Color-Swapping

From Tait Edge Colors to Four Face Colors

From Four Face Colors to Tait Edge Colors

Face Boundaries and Connectivity of the Dual

Defining the Plane Dual

Cycles and Cuts Across Planar Duals

Constructing Duals of Embedded Graphs

Computer-Assisted Proofs of the Four Color Theorem

Bridges, Loops, and Parallel Edges Under Duality

Bridge Obstructions to Cubic Edge Coloring