Borodin’s conjecture on diagonal coloring is false

In a 1-diagonal coloring, vertices of any face and vertices of any two faces sharing an edge have to get different colors. Borodin proved that any triangulation of a surface of Euler genus g≥1 can be 1-diagonally colored by ⌊13+73+48g2⌋ colors. The bound is conjectured to be sharp for all surfaces except for the sphere (g=0). We disprove this conjecture.