There are at least 3 nonhamiltonian MO-graphs with 16 vertices. In each case the chordless dominating cycle is 0-1-2-$\cdots$-11-0. Then vertices 12,13,14,15 are each adjacent to 3 vertices of the cycle, thus: (1) 2 3 4, 0 10 11, 6 7 8, 1 5 9 (2) 5 9 10, 2 3 8, 4 7 11, 0 1 6 (3) 3 4 10, 1 5 9, 2 7 8, 0 6 11 I didn't check them for 3-edge colourings.