  I argue that there is no 4-chromatic planar graph with a joinable pair of
color identical vertices, i.e., given a 4-chromatic planar graph G and a pair
of vertices {u, v} in G, if the color of u equals the color of v in every
4-coloring of G, then there is no planar supergraph of G where u and v are
adjacent. This is equivalent to the Four Color Theorem. (My argument is a
variation of my argument in arXiv:1402.7368)
