Consider the graph with 8 nodes A1, A2, A3, A4, H, T, F1, F2. Ai is
connected to Ai+1 for all i, each Ai is connected to H, H is connected to
T, and T is connected to each Fi. Find a 3-coloring of this graph by hand
using the following strategy: backtracking with conflict-directed
backjumping, the variable order A1, H, A4, F1, A2, F2, A3, T, and the
value order R, G, B.