New Graph

             [3, 3, 1, 1, 7, 7, 5, 5], [6, 8, 8, 6, 2, 4, 4, 2]

π = [1, 1, 1, 1, 1, 1, 1, 1]

POSSIBLE RANKS

1 x 8
2 x 4
NullSpace of Δ

{1, 3, 6, 8}, {2, 4, 5, 7}

Nullspace of A

[{2, 4},{5, 7}] `,` [{1, 3},{6, 8}]

1 . [1, 1, 1, 1, 1, 1, 1, 1]
"R", [3, 3, 1, 1, 7, 7, 5, 5]
"B", [6, 8, 8, 6, 2, 4, 4, 2]
"Coloring", {}

Delta Rank with R : 1 vs 4
Delta Rank with B : 1 vs 4

` See graph

` NOT SYNC'D

2 . [1, -1, 1, 1, 1, 1, 1, 1]
"R", [3, 8, 1, 1, 7, 7, 5, 5]
"B", [6, 3, 8, 6, 2, 4, 4, 2]
"Coloring", {2}

Delta Rank with R : 3 vs 5
Delta Rank with B : 3 vs 5

` See graph

` SYNC'D 15/2048

3 . [1, 1, -1, 1, 1, 1, 1, 1]
"R", [3, 3, 8, 1, 7, 7, 5, 5]
"B", [6, 8, 1, 6, 2, 4, 4, 2]
"Coloring", {3}

Delta Rank with R : 4 vs 5
Delta Rank with B : 3 vs 5

` See graph

` SYNC'D 5/512

4 . [1, 1, 1, -1, 1, 1, 1, 1]
"R", [3, 3, 1, 6, 7, 7, 5, 5]
"B", [6, 8, 8, 1, 2, 4, 4, 2]
"Coloring", {4}

Delta Rank with R : 3 vs 5
Delta Rank with B : 3 vs 5

` See graph

` SYNC'D 15/2048

5 . [1, 1, 1, 1, -1, 1, 1, 1]
"R", [3, 3, 1, 1, 2, 7, 5, 5]
"B", [6, 8, 8, 6, 7, 4, 4, 2]
"Coloring", {5}

Delta Rank with R : 4 vs 5
Delta Rank with B : 3 vs 5

` See graph

` SYNC'D 5/512

6 . [1, 1, 1, 1, 1, -1, 1, 1]
"R", [3, 3, 1, 1, 7, 4, 5, 5]
"B", [6, 8, 8, 6, 2, 7, 4, 2]
"Coloring", {6}

Delta Rank with R : 3 vs 5
Delta Rank with B : 3 vs 5

` See graph

` SYNC'D 15/2048

7 . [1, 1, 1, 1, 1, 1, -1, 1]
"R", [3, 3, 1, 1, 7, 7, 4, 5]
"B", [6, 8, 8, 6, 2, 4, 5, 2]
"Coloring", {7}

Delta Rank with R : 4 vs 5
Delta Rank with B : 3 vs 5

` See graph

` SYNC'D 5/512

8 . [1, 1, 1, 1, 1, 1, 1, -1]
"R", [3, 3, 1, 1, 7, 7, 5, 2]
"B", [6, 8, 8, 6, 2, 4, 4, 5]
"Coloring", {8}

Delta Rank with R : 3 vs 5
Delta Rank with B : 3 vs 5

` See graph

` SYNC'D 15/2048

9 . [1, -1, -1, 1, 1, 1, 1, 1]
"R", [3, 8, 8, 1, 7, 7, 5, 5]
"B", [6, 3, 1, 6, 2, 4, 4, 2]
"Coloring", {2, 3}

Delta Rank with R : 5 vs 5
Delta Rank with B : 5 vs 5

` See graph

` ---> RB-SYNC'D

10 . [1, -1, 1, -1, 1, 1, 1, 1]
"R", [3, 8, 1, 6, 7, 7, 5, 5]
"B", [6, 3, 8, 1, 2, 4, 4, 2]
"Coloring", {2, 4}

Delta Rank with R : "tailcheck for rank 6"
Delta Rank with B : 3 vs 6

` See graph

` NOT SYNC'D

11 . [1, -1, 1, 1, -1, 1, 1, 1]
"R", [3, 8, 1, 1, 2, 7, 5, 5]
"B", [6, 3, 8, 6, 7, 4, 4, 2]
"Coloring", {2, 5}

Delta Rank with R : 5 vs 6
Delta Rank with B : 3 vs 6

` See graph

` SYNC'D 2641/131072

12 . [1, -1, 1, 1, 1, -1, 1, 1]
"R", [3, 8, 1, 1, 7, 4, 5, 5]
"B", [6, 3, 8, 6, 2, 7, 4, 2]
"Coloring", {2, 6}

Delta Rank with R : "tailcheck for rank 6"
Delta Rank with B : 3 vs 6

` See graph

` NOT SYNC'D

13 . [1, -1, 1, 1, 1, 1, -1, 1]
"R", [3, 8, 1, 1, 7, 7, 4, 5]
"B", [6, 3, 8, 6, 2, 4, 5, 2]
"Coloring", {2, 7}

Delta Rank with R : 6 vs 6
Delta Rank with B : 5 vs 6

` See graph

` ---> RB-SYNC'D

14 . [1, -1, 1, 1, 1, 1, 1, -1]
"R", [3, 8, 1, 1, 7, 7, 5, 2]
"B", [6, 3, 8, 6, 2, 4, 4, 5]
"Coloring", {2, 8}

Delta Rank with R : 2 vs 6
Delta Rank with B : 1 vs 6

` See graph

` NOT SYNC'D

15 . [1, 1, -1, -1, 1, 1, 1, 1]
"R", [3, 3, 8, 6, 7, 7, 5, 5]
"B", [6, 8, 1, 1, 2, 4, 4, 2]
"Coloring", {3, 4}

Delta Rank with R : "tailcheck for rank 5"
Delta Rank with B : 4 vs 5

` See graph

` SYNC'D 1/16

16 . [1, 1, -1, 1, -1, 1, 1, 1]
"R", [3, 3, 8, 1, 2, 7, 5, 5]
"B", [6, 8, 1, 6, 7, 4, 4, 2]
"Coloring", {3, 5}

Delta Rank with R : "tailcheck for rank 6"
Delta Rank with B : "tailcheck for rank 6"

` See graph

` NOT SYNC'D

17 . [1, 1, -1, 1, 1, -1, 1, 1]
"R", [3, 3, 8, 1, 7, 4, 5, 5]
"B", [6, 8, 1, 6, 2, 7, 4, 2]
"Coloring", {3, 6}

Delta Rank with R : 6 vs 6
Delta Rank with B : 5 vs 6

` See graph

` ---> RB-SYNC'D

18 . [1, 1, -1, 1, 1, 1, -1, 1]
"R", [3, 3, 8, 1, 7, 7, 4, 5]
"B", [6, 8, 1, 6, 2, 4, 5, 2]
"Coloring", {3, 7}

Delta Rank with R : 3 vs 6
Delta Rank with B : "tailcheck for rank 6"

` See graph

` NOT SYNC'D

19 . [1, 1, -1, 1, 1, 1, 1, -1]
"R", [3, 3, 8, 1, 7, 7, 5, 2]
"B", [6, 8, 1, 6, 2, 4, 4, 5]
"Coloring", {3, 8}

Delta Rank with R : 5 vs 6
Delta Rank with B : 3 vs 6

` See graph

` SYNC'D 2641/131072

20 . [1, 1, 1, -1, -1, 1, 1, 1]
"R", [3, 3, 1, 6, 2, 7, 5, 5]
"B", [6, 8, 8, 1, 7, 4, 4, 2]
"Coloring", {4, 5}

Delta Rank with R : 6 vs 6
Delta Rank with B : 5 vs 6

` See graph

` ---> RB-SYNC'D

21 . [1, 1, 1, -1, 1, -1, 1, 1]
"R", [3, 3, 1, 6, 7, 4, 5, 5]
"B", [6, 8, 8, 1, 2, 7, 4, 2]
"Coloring", {4, 6}

Delta Rank with R : 2 vs 6
Delta Rank with B : 1 vs 6

` See graph

` NOT SYNC'D

22 . [1, 1, 1, -1, 1, 1, -1, 1]
"R", [3, 3, 1, 6, 7, 7, 4, 5]
"B", [6, 8, 8, 1, 2, 4, 5, 2]
"Coloring", {4, 7}

Delta Rank with R : 5 vs 6
Delta Rank with B : 3 vs 6

` See graph

` SYNC'D 2641/131072

23 . [1, 1, 1, -1, 1, 1, 1, -1]
"R", [3, 3, 1, 6, 7, 7, 5, 2]
"B", [6, 8, 8, 1, 2, 4, 4, 5]
"Coloring", {4, 8}

Delta Rank with R : "tailcheck for rank 6"
Delta Rank with B : 3 vs 6

` See graph

` NOT SYNC'D

24 . [1, 1, 1, 1, -1, -1, 1, 1]
"R", [3, 3, 1, 1, 2, 4, 5, 5]
"B", [6, 8, 8, 6, 7, 7, 4, 2]
"Coloring", {5, 6}

Delta Rank with R : "tailcheck for rank 5"
Delta Rank with B : 4 vs 5

` See graph

` SYNC'D 1/16

25 . [1, 1, 1, 1, -1, 1, -1, 1]
"R", [3, 3, 1, 1, 2, 7, 4, 5]
"B", [6, 8, 8, 6, 7, 4, 5, 2]
"Coloring", {5, 7}

Delta Rank with R : "tailcheck for rank 6"
Delta Rank with B : 2 vs 6

` See graph

` NOT SYNC'D

26 . [1, 1, 1, 1, -1, 1, 1, -1]
"R", [3, 3, 1, 1, 2, 7, 5, 2]
"B", [6, 8, 8, 6, 7, 4, 4, 5]
"Coloring", {5, 8}

Delta Rank with R : 5 vs 5
Delta Rank with B : 5 vs 5

` See graph

` ---> RB-SYNC'D

27 . [1, 1, 1, 1, 1, -1, -1, 1]
"R", [3, 3, 1, 1, 7, 4, 4, 5]
"B", [6, 8, 8, 6, 2, 7, 5, 2]
"Coloring", {6, 7}

Delta Rank with R : 5 vs 5
Delta Rank with B : 5 vs 5

` See graph

` ---> RB-SYNC'D

28 . [1, 1, 1, 1, 1, -1, 1, -1]
"R", [3, 3, 1, 1, 7, 4, 5, 2]
"B", [6, 8, 8, 6, 2, 7, 4, 5]
"Coloring", {6, 8}

Delta Rank with R : "tailcheck for rank 6"
Delta Rank with B : 3 vs 6

` See graph

` NOT SYNC'D

29 . [1, 1, 1, 1, 1, 1, -1, -1]
"R", [3, 3, 1, 1, 7, 7, 4, 2]
"B", [6, 8, 8, 6, 2, 4, 5, 5]
"Coloring", {7, 8}

Delta Rank with R : "tailcheck for rank 5"
Delta Rank with B : 4 vs 5

` See graph

` SYNC'D 1/16

30 . [1, -1, -1, -1, 1, 1, 1, 1]
"R", [3, 8, 8, 6, 7, 7, 5, 5]
"B", [6, 3, 1, 1, 2, 4, 4, 2]
"Coloring", {2, 3, 4}

Delta Rank with R : "tailcheck for rank 5"
Delta Rank with B : 5 vs 5

` See graph

` ---> RB-SYNC'D

31 . [1, -1, -1, 1, -1, 1, 1, 1]
"R", [3, 8, 8, 1, 2, 7, 5, 5]
"B", [6, 3, 1, 6, 7, 4, 4, 2]
"Coloring", {2, 3, 5}

Delta Rank with R : "tailcheck for rank 6"
Delta Rank with B : "tailcheck for rank 6"

` See graph

` SYNC'D 855/65536

32 . [1, -1, -1, 1, 1, -1, 1, 1]
"R", [3, 8, 8, 1, 7, 4, 5, 5]
"B", [6, 3, 1, 6, 2, 7, 4, 2]
"Coloring", {2, 3, 6}

Delta Rank with R : 5 vs 6
Delta Rank with B : 6 vs 6

` See graph

` ---> RB-SYNC'D

33 . [1, -1, -1, 1, 1, 1, -1, 1]
"R", [3, 8, 8, 1, 7, 7, 4, 5]
"B", [6, 3, 1, 6, 2, 4, 5, 2]
"Coloring", {2, 3, 7}

Delta Rank with R : 6 vs 6
Delta Rank with B : 5 vs 6

` See graph

` ---> RB-SYNC'D

34 . [1, -1, -1, 1, 1, 1, 1, -1]
"R", [3, 8, 8, 1, 7, 7, 5, 2]
"B", [6, 3, 1, 6, 2, 4, 4, 5]
"Coloring", {2, 3, 8}

Delta Rank with R : 4 vs 6
Delta Rank with B : 5 vs 6

` See graph

` SYNC'D 463/65536

35 . [1, -1, 1, -1, -1, 1, 1, 1]
"R", [3, 8, 1, 6, 2, 7, 5, 5]
"B", [6, 3, 8, 1, 7, 4, 4, 2]
"Coloring", {2, 4, 5}

Delta Rank with R : 3 vs 7
Delta Rank with B : 4 vs 7

` See graph

` SYNC'D 3999/262144

36 . [1, -1, 1, -1, 1, -1, 1, 1]
"R", [3, 8, 1, 6, 7, 4, 5, 5]
"B", [6, 3, 8, 1, 2, 7, 4, 2]
"Coloring", {2, 4, 6}

Delta Rank with R : 2 vs 7
Delta Rank with B : 3 vs 7

` See graph

` SYNC'D 145/131072

37 . [1, -1, 1, -1, 1, 1, -1, 1]
"R", [3, 8, 1, 6, 7, 7, 4, 5]
"B", [6, 3, 8, 1, 2, 4, 5, 2]
"Coloring", {2, 4, 7}

Delta Rank with R : 3 vs 7
Delta Rank with B : 4 vs 7

` See graph

` SYNC'D 3999/262144

38 . [1, -1, 1, -1, 1, 1, 1, -1]
"R", [3, 8, 1, 6, 7, 7, 5, 2]
"B", [6, 3, 8, 1, 2, 4, 4, 5]
"Coloring", {2, 4, 8}

Delta Rank with R : 2 vs 7
Delta Rank with B : 3 vs 7

` See graph

` SYNC'D 145/131072

39 . [1, -1, 1, 1, -1, -1, 1, 1]
"R", [3, 8, 1, 1, 2, 4, 5, 5]
"B", [6, 3, 8, 6, 7, 7, 4, 2]
"Coloring", {2, 5, 6}

Delta Rank with R : 4 vs 6
Delta Rank with B : 3 vs 6

` See graph

` SYNC'D 525/32768

40 . [1, -1, 1, 1, -1, 1, -1, 1]
"R", [3, 8, 1, 1, 2, 7, 4, 5]
"B", [6, 3, 8, 6, 7, 4, 5, 2]
"Coloring", {2, 5, 7}

Delta Rank with R : 4 vs 7
Delta Rank with B : 2 vs 7

` See graph

` SYNC'D 2469/262144

41 . [1, -1, 1, 1, -1, 1, 1, -1]
"R", [3, 8, 1, 1, 2, 7, 5, 2]
"B", [6, 3, 8, 6, 7, 4, 4, 5]
"Coloring", {2, 5, 8}

Delta Rank with R : 4 vs 6
Delta Rank with B : 5 vs 6

` See graph

` SYNC'D 463/65536

42 . [1, -1, 1, 1, 1, -1, -1, 1]
"R", [3, 8, 1, 1, 7, 4, 4, 5]
"B", [6, 3, 8, 6, 2, 7, 5, 2]
"Coloring", {2, 6, 7}

Delta Rank with R : 5 vs 6
Delta Rank with B : 6 vs 6

` See graph

` ---> RB-SYNC'D

43 . [1, -1, 1, 1, 1, -1, 1, -1]
"R", [3, 8, 1, 1, 7, 4, 5, 2]
"B", [6, 3, 8, 6, 2, 7, 4, 5]
"Coloring", {2, 6, 8}

Delta Rank with R : 2 vs 7
Delta Rank with B : 3 vs 7

` See graph

` SYNC'D 145/131072

44 . [1, -1, 1, 1, 1, 1, -1, -1]
"R", [3, 8, 1, 1, 7, 7, 4, 2]
"B", [6, 3, 8, 6, 2, 4, 5, 5]
"Coloring", {2, 7, 8}

Delta Rank with R : 4 vs 6
Delta Rank with B : 4 vs 6

` See graph

` SYNC'D 179/16384

45 . [1, 1, -1, -1, -1, 1, 1, 1]
"R", [3, 3, 8, 6, 2, 7, 5, 5]
"B", [6, 8, 1, 1, 7, 4, 4, 2]
"Coloring", {3, 4, 5}

Delta Rank with R : 6 vs 6
Delta Rank with B : 2 vs 6

` See graph

` ---> RB-SYNC'D

46 . [1, 1, -1, -1, 1, -1, 1, 1]
"R", [3, 3, 8, 6, 7, 4, 5, 5]
"B", [6, 8, 1, 1, 2, 7, 4, 2]
"Coloring", {3, 4, 6}

Delta Rank with R : 4 vs 6
Delta Rank with B : 4 vs 6

` See graph

` SYNC'D 179/16384

47 . [1, 1, -1, -1, 1, 1, -1, 1]
"R", [3, 3, 8, 6, 7, 7, 4, 5]
"B", [6, 8, 1, 1, 2, 4, 5, 2]
"Coloring", {3, 4, 7}

Delta Rank with R : 6 vs 6
Delta Rank with B : 4 vs 6

` See graph

` ---> RB-SYNC'D

48 . [1, 1, -1, -1, 1, 1, 1, -1]
"R", [3, 3, 8, 6, 7, 7, 5, 2]
"B", [6, 8, 1, 1, 2, 4, 4, 5]
"Coloring", {3, 4, 8}

Delta Rank with R : 4 vs 6
Delta Rank with B : 3 vs 6

` See graph

` SYNC'D 525/32768

49 . [1, 1, -1, 1, -1, -1, 1, 1]
"R", [3, 3, 8, 1, 2, 4, 5, 5]
"B", [6, 8, 1, 6, 7, 7, 4, 2]
"Coloring", {3, 5, 6}

Delta Rank with R : 6 vs 6
Delta Rank with B : 2 vs 6

` See graph

` ---> RB-SYNC'D

50 . [1, 1, -1, 1, -1, 1, -1, 1]
"R", [3, 3, 8, 1, 2, 7, 4, 5]
"B", [6, 8, 1, 6, 7, 4, 5, 2]
"Coloring", {3, 5, 7}

Delta Rank with R : 4 vs 7
Delta Rank with B : 2 vs 7

` See graph

` SYNC'D 285/262144

51 . [1, 1, -1, 1, -1, 1, 1, -1]
"R", [3, 3, 8, 1, 2, 7, 5, 2]
"B", [6, 8, 1, 6, 7, 4, 4, 5]
"Coloring", {3, 5, 8}

Delta Rank with R : "tailcheck for rank 6"
Delta Rank with B : "tailcheck for rank 6"

` See graph

` SYNC'D 855/65536

52 . [1, 1, -1, 1, 1, -1, -1, 1]
"R", [3, 3, 8, 1, 7, 4, 4, 5]
"B", [6, 8, 1, 6, 2, 7, 5, 2]
"Coloring", {3, 6, 7}

Delta Rank with R : 6 vs 6
Delta Rank with B : 5 vs 6

` See graph

` ---> RB-SYNC'D

53 . [1, 1, -1, 1, 1, -1, 1, -1]
"R", [3, 3, 8, 1, 7, 4, 5, 2]
"B", [6, 8, 1, 6, 2, 7, 4, 5]
"Coloring", {3, 6, 8}

Delta Rank with R : 3 vs 7
Delta Rank with B : 4 vs 7

` See graph

` SYNC'D 3999/262144

54 . [1, 1, -1, 1, 1, 1, -1, -1]
"R", [3, 3, 8, 1, 7, 7, 4, 2]
"B", [6, 8, 1, 6, 2, 4, 5, 5]
"Coloring", {3, 7, 8}

Delta Rank with R : 6 vs 6
Delta Rank with B : 4 vs 6

` See graph

` ---> RB-SYNC'D

55 . [1, 1, 1, -1, -1, -1, 1, 1]
"R", [3, 3, 1, 6, 2, 4, 5, 5]
"B", [6, 8, 8, 1, 7, 7, 4, 2]
"Coloring", {4, 5, 6}

Delta Rank with R : 4 vs 6
Delta Rank with B : 4 vs 6

` See graph

` SYNC'D 179/16384

56 . [1, 1, 1, -1, -1, 1, -1, 1]
"R", [3, 3, 1, 6, 2, 7, 4, 5]
"B", [6, 8, 8, 1, 7, 4, 5, 2]
"Coloring", {4, 5, 7}

Delta Rank with R : 4 vs 7
Delta Rank with B : 2 vs 7

` See graph

` SYNC'D 2469/262144

57 . [1, 1, 1, -1, -1, 1, 1, -1]
"R", [3, 3, 1, 6, 2, 7, 5, 2]
"B", [6, 8, 8, 1, 7, 4, 4, 5]
"Coloring", {4, 5, 8}

Delta Rank with R : 5 vs 6
Delta Rank with B : 6 vs 6

` See graph

` ---> RB-SYNC'D

58 . [1, 1, 1, -1, 1, -1, -1, 1]
"R", [3, 3, 1, 6, 7, 4, 4, 5]
"B", [6, 8, 8, 1, 2, 7, 5, 2]
"Coloring", {4, 6, 7}

Delta Rank with R : 4 vs 6
Delta Rank with B : 5 vs 6

` See graph

` SYNC'D 463/65536

59 . [1, 1, 1, -1, 1, -1, 1, -1]
"R", [3, 3, 1, 6, 7, 4, 5, 2]
"B", [6, 8, 8, 1, 2, 7, 4, 5]
"Coloring", {4, 6, 8}

Delta Rank with R : 2 vs 7
Delta Rank with B : 3 vs 7

` See graph

` SYNC'D 145/131072

60 . [1, 1, 1, -1, 1, 1, -1, -1]
"R", [3, 3, 1, 6, 7, 7, 4, 2]
"B", [6, 8, 8, 1, 2, 4, 5, 5]
"Coloring", {4, 7, 8}

Delta Rank with R : 4 vs 6
Delta Rank with B : 3 vs 6

` See graph

` SYNC'D 525/32768

61 . [1, 1, 1, 1, -1, -1, -1, 1]
"R", [3, 3, 1, 1, 2, 4, 4, 5]
"B", [6, 8, 8, 6, 7, 7, 5, 2]
"Coloring", {5, 6, 7}

Delta Rank with R : "tailcheck for rank 5"
Delta Rank with B : 3 vs 5

` See graph

` SYNC'D 9/256

62 . [1, 1, 1, 1, -1, -1, 1, -1]
"R", [3, 3, 1, 1, 2, 4, 5, 2]
"B", [6, 8, 8, 6, 7, 7, 4, 5]
"Coloring", {5, 6, 8}

Delta Rank with R : "tailcheck for rank 5"
Delta Rank with B : 5 vs 5

` See graph

` ---> RB-SYNC'D

63 . [1, 1, 1, 1, -1, 1, -1, -1]
"R", [3, 3, 1, 1, 2, 7, 4, 2]
"B", [6, 8, 8, 6, 7, 4, 5, 5]
"Coloring", {5, 7, 8}

Delta Rank with R : "tailcheck for rank 5"
Delta Rank with B : 3 vs 5

` See graph

` SYNC'D 9/256

64 . [1, 1, 1, 1, 1, -1, -1, -1]
"R", [3, 3, 1, 1, 7, 4, 4, 2]
"B", [6, 8, 8, 6, 2, 7, 5, 5]
"Coloring", {6, 7, 8}

Delta Rank with R : "tailcheck for rank 5"
Delta Rank with B : 5 vs 5

` See graph

` ---> RB-SYNC'D

65 . [1, -1, -1, -1, -1, 1, 1, 1]
"R", [3, 8, 8, 6, 2, 7, 5, 5]
"B", [6, 3, 1, 1, 7, 4, 4, 2]
"Coloring", {2, 3, 4, 5}

Delta Rank with R : "tailcheck for rank 6"
Delta Rank with B : "tailcheck for rank 6"

` See graph

` SYNC'D 1269/32768

66 . [1, -1, -1, -1, 1, -1, 1, 1]
"R", [3, 8, 8, 6, 7, 4, 5, 5]
"B", [6, 3, 1, 1, 2, 7, 4, 2]
"Coloring", {2, 3, 4, 6}

Delta Rank with R : 3 vs 6
Delta Rank with B : 6 vs 6

` See graph

` ---> RB-SYNC'D

67 . [1, -1, -1, -1, 1, 1, -1, 1]
"R", [3, 8, 8, 6, 7, 7, 4, 5]
"B", [6, 3, 1, 1, 2, 4, 5, 2]
"Coloring", {2, 3, 4, 7}

Delta Rank with R : 6 vs 6
Delta Rank with B : 6 vs 6

` See graph

` ---> RB-SYNC'D

68 . [1, -1, -1, -1, 1, 1, 1, -1]
"R", [3, 8, 8, 6, 7, 7, 5, 2]
"B", [6, 3, 1, 1, 2, 4, 4, 5]
"Coloring", {2, 3, 4, 8}

Delta Rank with R : "tailcheck for rank 6"
Delta Rank with B : 6 vs 6

` See graph

` ---> RB-SYNC'D

69 . [1, -1, -1, 1, -1, -1, 1, 1]
"R", [3, 8, 8, 1, 2, 4, 5, 5]
"B", [6, 3, 1, 6, 7, 7, 4, 2]
"Coloring", {2, 3, 5, 6}

Delta Rank with R : 6 vs 6
Delta Rank with B : 6 vs 6

` See graph

` ---> RB-SYNC'D

70 . [1, -1, -1, 1, -1, 1, -1, 1]
"R", [3, 8, 8, 1, 2, 7, 4, 5]
"B", [6, 3, 1, 6, 7, 4, 5, 2]
"Coloring", {2, 3, 5, 7}

Delta Rank with R : 7 vs 7
Delta Rank with B : 4 vs 7

` See graph

` ---> RB-SYNC'D

71 . [1, -1, -1, 1, -1, 1, 1, -1]
"R", [3, 8, 8, 1, 2, 7, 5, 2]
"B", [6, 3, 1, 6, 7, 4, 4, 5]
"Coloring", {2, 3, 5, 8}

Delta Rank with R : "tailcheck for rank 6"
Delta Rank with B : "tailcheck for rank 6"

` See graph

` NOT SYNC'D

72 . [1, -1, -1, 1, 1, -1, -1, 1]
"R", [3, 8, 8, 1, 7, 4, 4, 5]
"B", [6, 3, 1, 6, 2, 7, 5, 2]
"Coloring", {2, 3, 6, 7}

Delta Rank with R : 3 vs 6
Delta Rank with B : 3 vs 6

` See graph

` NOT SYNC'D

73 . [1, -1, -1, 1, 1, -1, 1, -1]
"R", [3, 8, 8, 1, 7, 4, 5, 2]
"B", [6, 3, 1, 6, 2, 7, 4, 5]
"Coloring", {2, 3, 6, 8}

Delta Rank with R : 4 vs 7
Delta Rank with B : 7 vs 7

` See graph

` ---> RB-SYNC'D

74 . [1, -1, -1, 1, 1, 1, -1, -1]
"R", [3, 8, 8, 1, 7, 7, 4, 2]
"B", [6, 3, 1, 6, 2, 4, 5, 5]
"Coloring", {2, 3, 7, 8}

Delta Rank with R : 6 vs 6
Delta Rank with B : 6 vs 6

` See graph

` ---> RB-SYNC'D

75 . [1, -1, 1, -1, -1, -1, 1, 1]
"R", [3, 8, 1, 6, 2, 4, 5, 5]
"B", [6, 3, 8, 1, 7, 7, 4, 2]
"Coloring", {2, 4, 5, 6}

Delta Rank with R : 3 vs 7
Delta Rank with B : 4 vs 7

` See graph

` SYNC'D 19/2048

76 . [1, -1, 1, -1, -1, 1, -1, 1]
"R", [3, 8, 1, 6, 2, 7, 4, 5]
"B", [6, 3, 8, 1, 7, 4, 5, 2]
"Coloring", {2, 4, 5, 7}

Delta Rank with R : 1 vs 8
Delta Rank with B : 1 vs 8

` See graph

` NOT SYNC'D

77 . [1, -1, 1, -1, -1, 1, 1, -1]
"R", [3, 8, 1, 6, 2, 7, 5, 2]
"B", [6, 3, 8, 1, 7, 4, 4, 5]
"Coloring", {2, 4, 5, 8}

Delta Rank with R : 4 vs 7
Delta Rank with B : 7 vs 7

` See graph

` ---> RB-SYNC'D

78 . [1, -1, 1, -1, 1, -1, -1, 1]
"R", [3, 8, 1, 6, 7, 4, 4, 5]
"B", [6, 3, 8, 1, 2, 7, 5, 2]
"Coloring", {2, 4, 6, 7}

Delta Rank with R : 4 vs 7
Delta Rank with B : 7 vs 7

` See graph

` ---> RB-SYNC'D

79 . [1, -1, 1, -1, 1, -1, 1, -1]
"R", [3, 8, 1, 6, 7, 4, 5, 2]
"B", [6, 3, 8, 1, 2, 7, 4, 5]
"Coloring", {2, 4, 6, 8}

Delta Rank with R : 1 vs 8
Delta Rank with B : 1 vs 8

` See graph

` NOT SYNC'D

80 . [1, -1, 1, -1, 1, 1, -1, -1]
"R", [3, 8, 1, 6, 7, 7, 4, 2]
"B", [6, 3, 8, 1, 2, 4, 5, 5]
"Coloring", {2, 4, 7, 8}

Delta Rank with R : 3 vs 7
Delta Rank with B : 4 vs 7

` See graph

` SYNC'D 19/2048

81 . [1, -1, 1, 1, -1, -1, -1, 1]
"R", [3, 8, 1, 1, 2, 4, 4, 5]
"B", [6, 3, 8, 6, 7, 7, 5, 2]
"Coloring", {2, 5, 6, 7}

Delta Rank with R : 3 vs 6
Delta Rank with B : 3 vs 6

` See graph

` SYNC'D 1125/32768

82 . [1, -1, 1, 1, -1, -1, 1, -1]
"R", [3, 8, 1, 1, 2, 4, 5, 2]
"B", [6, 3, 8, 6, 7, 7, 4, 5]
"Coloring", {2, 5, 6, 8}

Delta Rank with R : "tailcheck for rank 6"
Delta Rank with B : 6 vs 6

` See graph

` ---> RB-SYNC'D

83 . [1, -1, 1, 1, -1, 1, -1, -1]
"R", [3, 8, 1, 1, 2, 7, 4, 2]
"B", [6, 3, 8, 6, 7, 4, 5, 5]
"Coloring", {2, 5, 7, 8}

Delta Rank with R : 4 vs 6
Delta Rank with B : 4 vs 6

` See graph

` SYNC'D 99/16384

84 . [1, -1, 1, 1, 1, -1, -1, -1]
"R", [3, 8, 1, 1, 7, 4, 4, 2]
"B", [6, 3, 8, 6, 2, 7, 5, 5]
"Coloring", {2, 6, 7, 8}

Delta Rank with R : 3 vs 6
Delta Rank with B : 6 vs 6

` See graph

` ---> RB-SYNC'D

85 . [1, 1, -1, -1, -1, -1, 1, 1]
"R", [3, 3, 8, 6, 2, 4, 5, 5]
"B", [6, 8, 1, 1, 7, 7, 4, 2]
"Coloring", {3, 4, 5, 6}

Delta Rank with R : 2 vs 6
Delta Rank with B : 2 vs 6

` See graph

` NOT SYNC'D

86 . [1, 1, -1, -1, -1, 1, -1, 1]
"R", [3, 3, 8, 6, 2, 7, 4, 5]
"B", [6, 8, 1, 1, 7, 4, 5, 2]
"Coloring", {3, 4, 5, 7}

Delta Rank with R : 4 vs 7
Delta Rank with B : 3 vs 7

` See graph

` SYNC'D 19/2048

87 . [1, 1, -1, -1, -1, 1, 1, -1]
"R", [3, 3, 8, 6, 2, 7, 5, 2]
"B", [6, 8, 1, 1, 7, 4, 4, 5]
"Coloring", {3, 4, 5, 8}

Delta Rank with R : 6 vs 6
Delta Rank with B : 6 vs 6

` See graph

` ---> RB-SYNC'D

88 . [1, 1, -1, -1, 1, -1, -1, 1]
"R", [3, 3, 8, 6, 7, 4, 4, 5]
"B", [6, 8, 1, 1, 2, 7, 5, 2]
"Coloring", {3, 4, 6, 7}

Delta Rank with R : 6 vs 6
Delta Rank with B : 6 vs 6

` See graph

` ---> RB-SYNC'D

89 . [1, 1, -1, -1, 1, -1, 1, -1]
"R", [3, 3, 8, 6, 7, 4, 5, 2]
"B", [6, 8, 1, 1, 2, 7, 4, 5]
"Coloring", {3, 4, 6, 8}

Delta Rank with R : 3 vs 7
Delta Rank with B : 4 vs 7

` See graph

` SYNC'D 19/2048

90 . [1, 1, -1, -1, 1, 1, -1, -1]
"R", [3, 3, 8, 6, 7, 7, 4, 2]
"B", [6, 8, 1, 1, 2, 4, 5, 5]
"Coloring", {3, 4, 7, 8}

Delta Rank with R : 3 vs 6
Delta Rank with B : 3 vs 6

` See graph

` NOT SYNC'D

91 . [1, 1, -1, 1, -1, -1, -1, 1]
"R", [3, 3, 8, 1, 2, 4, 4, 5]
"B", [6, 8, 1, 6, 7, 7, 5, 2]
"Coloring", {3, 5, 6, 7}

Delta Rank with R : 6 vs 6
Delta Rank with B : 3 vs 6

` See graph

` ---> RB-SYNC'D

92 . [1, 1, -1, 1, -1, -1, 1, -1]
"R", [3, 3, 8, 1, 2, 4, 5, 2]
"B", [6, 8, 1, 6, 7, 7, 4, 5]
"Coloring", {3, 5, 6, 8}

Delta Rank with R : "tailcheck for rank 6"
Delta Rank with B : "tailcheck for rank 6"

` See graph

` SYNC'D 1269/32768

93 . [1, 1, -1, 1, -1, 1, -1, -1]
"R", [3, 3, 8, 1, 2, 7, 4, 2]
"B", [6, 8, 1, 6, 7, 4, 5, 5]
"Coloring", {3, 5, 7, 8}

Delta Rank with R : 6 vs 6
Delta Rank with B : "tailcheck for rank 6"

` See graph

` ---> RB-SYNC'D

94 . [1, 1, -1, 1, 1, -1, -1, -1]
"R", [3, 3, 8, 1, 7, 4, 4, 2]
"B", [6, 8, 1, 6, 2, 7, 5, 5]
"Coloring", {3, 6, 7, 8}

Delta Rank with R : 6 vs 6
Delta Rank with B : 6 vs 6

` See graph

` ---> RB-SYNC'D

95 . [1, 1, 1, -1, -1, -1, -1, 1]
"R", [3, 3, 1, 6, 2, 4, 4, 5]
"B", [6, 8, 8, 1, 7, 7, 5, 2]
"Coloring", {4, 5, 6, 7}

Delta Rank with R : 4 vs 6
Delta Rank with B : 4 vs 6

` See graph

` SYNC'D 99/16384

96 . [1, 1, 1, -1, -1, -1, 1, -1]
"R", [3, 3, 1, 6, 2, 4, 5, 2]
"B", [6, 8, 8, 1, 7, 7, 4, 5]
"Coloring", {4, 5, 6, 8}

Delta Rank with R : 3 vs 6
Delta Rank with B : 6 vs 6

` See graph

` ---> RB-SYNC'D

97 . [1, 1, 1, -1, -1, 1, -1, -1]
"R", [3, 3, 1, 6, 2, 7, 4, 2]
"B", [6, 8, 8, 1, 7, 4, 5, 5]
"Coloring", {4, 5, 7, 8}

Delta Rank with R : 3 vs 6
Delta Rank with B : 3 vs 6

` See graph

` SYNC'D 1125/32768

98 . [1, 1, 1, -1, 1, -1, -1, -1]
"R", [3, 3, 1, 6, 7, 4, 4, 2]
"B", [6, 8, 8, 1, 2, 7, 5, 5]
"Coloring", {4, 6, 7, 8}

Delta Rank with R : "tailcheck for rank 6"
Delta Rank with B : 6 vs 6

` See graph

` ---> RB-SYNC'D

99 . [1, 1, 1, 1, -1, -1, -1, -1]
"R", [3, 3, 1, 1, 2, 4, 4, 2]
"B", [6, 8, 8, 6, 7, 7, 5, 5]
"Coloring", {5, 6, 7, 8}

Delta Rank with R : "tailcheck for rank 4"
Delta Rank with B : "tailcheck for rank 4"

` See graph

` NOT SYNC'D

100 . [1, -1, -1, -1, -1, -1, 1, 1]
"R", [3, 8, 8, 6, 2, 4, 5, 5]
"B", [6, 3, 1, 1, 7, 7, 4, 2]
"Coloring", {2, 3, 4, 5, 6}

Delta Rank with R : 2 vs 6
Delta Rank with B : 6 vs 6

` See graph

` ---> RB-SYNC'D

101 . [1, -1, -1, -1, -1, 1, -1, 1]
"R", [3, 8, 8, 6, 2, 7, 4, 5]
"B", [6, 3, 1, 1, 7, 4, 5, 2]
"Coloring", {2, 3, 4, 5, 7}

Delta Rank with R : 4 vs 7
Delta Rank with B : 3 vs 7

` See graph

` SYNC'D 3999/262144

102 . [1, -1, -1, -1, -1, 1, 1, -1]
"R", [3, 8, 8, 6, 2, 7, 5, 2]
"B", [6, 3, 1, 1, 7, 4, 4, 5]
"Coloring", {2, 3, 4, 5, 8}

Delta Rank with R : "tailcheck for rank 6"
Delta Rank with B : "tailcheck for rank 6"

` See graph

` SYNC'D 855/65536

103 . [1, -1, -1, -1, 1, -1, -1, 1]
"R", [3, 8, 8, 6, 7, 4, 4, 5]
"B", [6, 3, 1, 1, 2, 7, 5, 2]
"Coloring", {2, 3, 4, 6, 7}

Delta Rank with R : 5 vs 6
Delta Rank with B : 6 vs 6

` See graph

` ---> RB-SYNC'D

104 . [1, -1, -1, -1, 1, -1, 1, -1]
"R", [3, 8, 8, 6, 7, 4, 5, 2]
"B", [6, 3, 1, 1, 2, 7, 4, 5]
"Coloring", {2, 3, 4, 6, 8}

Delta Rank with R : 2 vs 7
Delta Rank with B : 4 vs 7

` See graph

` SYNC'D 285/262144

105 . [1, -1, -1, -1, 1, 1, -1, -1]
"R", [3, 8, 8, 6, 7, 7, 4, 2]
"B", [6, 3, 1, 1, 2, 4, 5, 5]
"Coloring", {2, 3, 4, 7, 8}

Delta Rank with R : 4 vs 6
Delta Rank with B : 6 vs 6

` See graph

` ---> RB-SYNC'D

106 . [1, -1, -1, 1, -1, -1, -1, 1]
"R", [3, 8, 8, 1, 2, 4, 4, 5]
"B", [6, 3, 1, 6, 7, 7, 5, 2]
"Coloring", {2, 3, 5, 6, 7}

Delta Rank with R : 6 vs 6
Delta Rank with B : 5 vs 6

` See graph

` ---> RB-SYNC'D

107 . [1, -1, -1, 1, -1, -1, 1, -1]
"R", [3, 8, 8, 1, 2, 4, 5, 2]
"B", [6, 3, 1, 6, 7, 7, 4, 5]
"Coloring", {2, 3, 5, 6, 8}

Delta Rank with R : "tailcheck for rank 6"
Delta Rank with B : "tailcheck for rank 6"

` See graph

` SYNC'D 855/65536

108 . [1, -1, -1, 1, -1, 1, -1, -1]
"R", [3, 8, 8, 1, 2, 7, 4, 2]
"B", [6, 3, 1, 6, 7, 4, 5, 5]
"Coloring", {2, 3, 5, 7, 8}

Delta Rank with R : 5 vs 6
Delta Rank with B : 4 vs 6

` See graph

` SYNC'D 463/65536

109 . [1, -1, -1, 1, 1, -1, -1, -1]
"R", [3, 8, 8, 1, 7, 4, 4, 2]
"B", [6, 3, 1, 6, 2, 7, 5, 5]
"Coloring", {2, 3, 6, 7, 8}

Delta Rank with R : 5 vs 6
Delta Rank with B : 6 vs 6

` See graph

` ---> RB-SYNC'D

110 . [1, -1, 1, -1, -1, -1, -1, 1]
"R", [3, 8, 1, 6, 2, 4, 4, 5]
"B", [6, 3, 8, 1, 7, 7, 5, 2]
"Coloring", {2, 4, 5, 6, 7}

Delta Rank with R : 2 vs 7
Delta Rank with B : 4 vs 7

` See graph

` SYNC'D 2469/262144

111 . [1, -1, 1, -1, -1, -1, 1, -1]
"R", [3, 8, 1, 6, 2, 4, 5, 2]
"B", [6, 3, 8, 1, 7, 7, 4, 5]
"Coloring", {2, 4, 5, 6, 8}

Delta Rank with R : 2 vs 7
Delta Rank with B : 4 vs 7

` See graph

` SYNC'D 285/262144

112 . [1, -1, 1, -1, -1, 1, -1, -1]
"R", [3, 8, 1, 6, 2, 7, 4, 2]
"B", [6, 3, 8, 1, 7, 4, 5, 5]
"Coloring", {2, 4, 5, 7, 8}

Delta Rank with R : 2 vs 7
Delta Rank with B : 4 vs 7

` See graph

` SYNC'D 2469/262144

113 . [1, -1, 1, -1, 1, -1, -1, -1]
"R", [3, 8, 1, 6, 7, 4, 4, 2]
"B", [6, 3, 8, 1, 2, 7, 5, 5]
"Coloring", {2, 4, 6, 7, 8}

Delta Rank with R : 2 vs 7
Delta Rank with B : 4 vs 7

` See graph

` SYNC'D 285/262144

114 . [1, -1, 1, 1, -1, -1, -1, -1]
"R", [3, 8, 1, 1, 2, 4, 4, 2]
"B", [6, 3, 8, 6, 7, 7, 5, 5]
"Coloring", {2, 5, 6, 7, 8}

Delta Rank with R : 3 vs 5
Delta Rank with B : "tailcheck for rank 5"

` See graph

` SYNC'D 9/256

115 . [1, 1, -1, -1, -1, -1, -1, 1]
"R", [3, 3, 8, 6, 2, 4, 4, 5]
"B", [6, 8, 1, 1, 7, 7, 5, 2]
"Coloring", {3, 4, 5, 6, 7}

Delta Rank with R : 4 vs 6
Delta Rank with B : 4 vs 6

` See graph

` SYNC'D 179/16384

116 . [1, 1, -1, -1, -1, -1, 1, -1]
"R", [3, 3, 8, 6, 2, 4, 5, 2]
"B", [6, 8, 1, 1, 7, 7, 4, 5]
"Coloring", {3, 4, 5, 6, 8}

Delta Rank with R : 2 vs 6
Delta Rank with B : 6 vs 6

` See graph

` ---> RB-SYNC'D

117 . [1, 1, -1, -1, -1, 1, -1, -1]
"R", [3, 3, 8, 6, 2, 7, 4, 2]
"B", [6, 8, 1, 1, 7, 4, 5, 5]
"Coloring", {3, 4, 5, 7, 8}

Delta Rank with R : 3 vs 6
Delta Rank with B : 4 vs 6

` See graph

` SYNC'D 525/32768

118 . [1, 1, -1, -1, 1, -1, -1, -1]
"R", [3, 3, 8, 6, 7, 4, 4, 2]
"B", [6, 8, 1, 1, 2, 7, 5, 5]
"Coloring", {3, 4, 6, 7, 8}

Delta Rank with R : 4 vs 6
Delta Rank with B : 6 vs 6

` See graph

` ---> RB-SYNC'D

119 . [1, 1, -1, 1, -1, -1, -1, -1]
"R", [3, 3, 8, 1, 2, 4, 4, 2]
"B", [6, 8, 1, 6, 7, 7, 5, 5]
"Coloring", {3, 5, 6, 7, 8}

Delta Rank with R : 5 vs 5
Delta Rank with B : "tailcheck for rank 5"

` See graph

` ---> RB-SYNC'D

120 . [1, 1, 1, -1, -1, -1, -1, -1]
"R", [3, 3, 1, 6, 2, 4, 4, 2]
"B", [6, 8, 8, 1, 7, 7, 5, 5]
"Coloring", {4, 5, 6, 7, 8}

Delta Rank with R : 3 vs 5
Delta Rank with B : "tailcheck for rank 5"

` See graph

` SYNC'D 9/256

121 . [1, -1, -1, -1, -1, -1, -1, 1]
"R", [3, 8, 8, 6, 2, 4, 4, 5]
"B", [6, 3, 1, 1, 7, 7, 5, 2]
"Coloring", {2, 3, 4, 5, 6, 7}

Delta Rank with R : 5 vs 6
Delta Rank with B : 6 vs 6

` See graph

` ---> RB-SYNC'D

122 . [1, -1, -1, -1, -1, -1, 1, -1]
"R", [3, 8, 8, 6, 2, 4, 5, 2]
"B", [6, 3, 1, 1, 7, 7, 4, 5]
"Coloring", {2, 3, 4, 5, 6, 8}

Delta Rank with R : "tailcheck for rank 6"
Delta Rank with B : "tailcheck for rank 6"

` See graph

` NOT SYNC'D

123 . [1, -1, -1, -1, -1, 1, -1, -1]
"R", [3, 8, 8, 6, 2, 7, 4, 2]
"B", [6, 3, 1, 1, 7, 4, 5, 5]
"Coloring", {2, 3, 4, 5, 7, 8}

Delta Rank with R : 3 vs 6
Delta Rank with B : 5 vs 6

` See graph

` SYNC'D 2641/131072

124 . [1, -1, -1, -1, 1, -1, -1, -1]
"R", [3, 8, 8, 6, 7, 4, 4, 2]
"B", [6, 3, 1, 1, 2, 7, 5, 5]
"Coloring", {2, 3, 4, 6, 7, 8}

Delta Rank with R : "tailcheck for rank 6"
Delta Rank with B : 3 vs 6

` See graph

` NOT SYNC'D

125 . [1, -1, -1, 1, -1, -1, -1, -1]
"R", [3, 8, 8, 1, 2, 4, 4, 2]
"B", [6, 3, 1, 6, 7, 7, 5, 5]
"Coloring", {2, 3, 5, 6, 7, 8}

Delta Rank with R : 5 vs 5
Delta Rank with B : 5 vs 5

` See graph

` ---> RB-SYNC'D

126 . [1, -1, 1, -1, -1, -1, -1, -1]
"R", [3, 8, 1, 6, 2, 4, 4, 2]
"B", [6, 3, 8, 1, 7, 7, 5, 5]
"Coloring", {2, 4, 5, 6, 7, 8}

Delta Rank with R : 2 vs 6
Delta Rank with B : "tailcheck for rank 6"

` See graph

` NOT SYNC'D

127 . [1, 1, -1, -1, -1, -1, -1, -1]
"R", [3, 3, 8, 6, 2, 4, 4, 2]
"B", [6, 8, 1, 1, 7, 7, 5, 5]
"Coloring", {3, 4, 5, 6, 7, 8}

Delta Rank with R : 4 vs 5
Delta Rank with B : "tailcheck for rank 5"

` See graph

` SYNC'D 1/16

128 . [1, -1, -1, -1, -1, -1, -1, -1]
"R", [3, 8, 8, 6, 2, 4, 4, 2]
"B", [6, 3, 1, 1, 7, 7, 5, 5]
"Coloring", {2, 3, 4, 5, 6, 7, 8}

Delta Rank with R : 3 vs 5
Delta Rank with B : 4 vs 5

` See graph

` SYNC'D 5/512

SUMMARY

Graph Type
CC

ν(A)
2

ν(Δ)
2

π
[1, 1, 1, 1, 1, 1, 1, 1]

Dbly Stoch
true

SUMMARY
Graph Type		CC
ν(A)		2
ν(Δ)		2
π		[1, 1, 1, 1, 1, 1, 1, 1]
Dbly Stoch		true

SANDWICH
Total 0

No . Coloring Rank

SANDWICH		Total 0
No .	Coloring	Rank

RT GROUPS
Total 0

No . Coloring Rank Solv

RT GROUPS		Total 0
No .	Coloring	Rank	Solv

RANK'D SYNC'D NOT RANK'D τ-RANK'D NOT SYNC'D Total Runs 2^n-1
0 0 46 20 128 128