exhaustive n=4: 46656 monotone graph systems (all up-set label families), k in [1, 2, 3]
  outcomes: {1: {'colouring': 1, 'star': 46655}, 2: {'colouring': 32346, 'star': 14310}, 3: {'colouring': 46611, 'star': 45}}
  all outputs verified (colouring into k independent sets, or a good k-star) 
random n=5 trials=2000 seed=5: all outputs verified; {(1, 'colouring'): 176, (1, 'star'): 1824, (2, 'colouring'): 1342, (2, 'star'): 658, (3, 'colouring'): 1961, (3, 'star'): 39, (4, 'colouring'): 1998, (4, 'star'): 2}
random n=6 trials=2000 seed=6: all outputs verified; {(1, 'colouring'): 134, (1, 'star'): 1866, (2, 'colouring'): 1168, (2, 'star'): 832, (3, 'colouring'): 1918, (3, 'star'): 82, (4, 'colouring'): 1999, (4, 'star'): 1, (5, 'colouring'): 2000}
random n=7 trials=2000 seed=7: all outputs verified; {(1, 'colouring'): 93, (1, 'star'): 1907, (2, 'colouring'): 1029, (2, 'star'): 971, (3, 'colouring'): 1848, (3, 'star'): 152, (4, 'colouring'): 1999, (4, 'star'): 1, (5, 'colouring'): 2000, (6, 'colouring'): 2000}
random n=8 trials=2000 seed=8: all outputs verified; {(1, 'colouring'): 81, (1, 'star'): 1919, (2, 'colouring'): 898, (2, 'star'): 1102, (3, 'colouring'): 1824, (3, 'star'): 176, (4, 'colouring'): 1994, (4, 'star'): 6, (5, 'colouring'): 2000, (6, 'colouring'): 2000, (7, 'colouring'): 2000}
random 2-iatlon graphs on kb+1=5 vertices, k=2: 200 trials, a verified constrained K_1,2 returned every time
random 3-iatlon graphs on kb+1=10 vertices, k=3: 200 trials, a verified constrained K_1,3 returned every time
random 3-iatlon graphs on kb+1=13 vertices, k=4: 200 trials, a verified constrained K_1,4 returned every time
