Single node of degree 4

We prove this configuration colorable:

We color the boundary nodes with all 4 possible color combinations, modulo equivalence of colors.

3 successes are simple and 1 requires 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.)