Birkhoff diamond

We prove this configuration colorable:

(A planar graph)

We color the boundary nodes with all 6 possible color combinations, modulo equivalence of colors, that are consistent with this smaller configuration:

(A planar graph)

4 successes are simple and 2 require Kempe-chains.

Easily colorable boundary node color-arrangements

Kempe chain possibilities for RB/GY on

with color-flipped boundary nodes marked with heavy dashes. (Apologies for the kempe chain edges passing through things visually.)

(A planar graph)

(A planar graph)

(A planar graph)

(A planar graph)

(A planar graph)

(A planar graph)

(A planar graph)

(A planar graph)

(A planar graph)

(A planar graph)

(A planar graph)

(A planar graph)

Kempe chain possibilities for RY/BG on

with color-flipped boundary nodes marked with heavy dashes. (Apologies for the kempe chain edges passing through things visually.)

(A planar graph)

(A planar graph)

(A planar graph)

(A planar graph)

(A planar graph)

(A planar graph)

(A planar graph)

(A planar graph)

(A planar graph)

(A planar graph)

(A planar graph)

(A planar graph)