New Graph

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

π = [1, 2, 2, 3, 2, 2]

POSSIBLE RANKS

1 x 12
2 x 6
3 x 4
NullSpace of Δ

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

Nullspace of A

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

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

Delta Rank with R : 1 vs 4
Delta Rank with B : 3 vs 5

` See graph

` NOT SYNC'D

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

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

` See graph

` ---> RB-SYNC'D

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

Delta Rank with R : 2 vs 4
Delta Rank with B : "tailcheck for rank 4"

` See graph

` NOT SYNC'D

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

Delta Rank with R : 2 vs 5
Delta Rank with B : 3 vs 6

` See graph

` NOT SYNC'D

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

Delta Rank with R : 3 vs 4
Delta Rank with B : 2 vs 4

` See graph

` NOT SYNC'D

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

Delta Rank with R : 2 vs 3
Delta Rank with B : 4 vs 4

` See graph

` ---> RB-SYNC'D

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

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

` See graph

` ---> RB-SYNC'D

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

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

` See graph

` SYNC'D 5/256

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

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

` See graph

` SYNC'D 3/32

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

Delta Rank with R : 1 vs 3
Delta Rank with B : 2 vs 4

` See graph

` NOT SYNC'D

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

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

` See graph

` ---> RB-SYNC'D

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

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

` See graph

` ---> RB-SYNC'D

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

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

` See graph

` SYNC'D 3/32

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

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

` See graph

` ---> RB-SYNC'D

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

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

` See graph

` ---> RB-SYNC'D

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

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

` See graph

` ---> RB-SYNC'D

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

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

` See graph

` ---> RB-SYNC'D

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

Delta Rank with R : 2 vs 4
Delta Rank with B : 2 vs 3

` See graph

` NOT SYNC'D

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

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

` See graph

` ---> RB-SYNC'D

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

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

` See graph

` SYNC'D 3/128

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

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

` See graph

` ---> RB-SYNC'D

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

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

` See graph

` ---> RB-SYNC'D

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

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

` See graph

` ---> RB-SYNC'D

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

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

` See graph

` SYNC'D 9/256

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

Delta Rank with R : 3 vs 4
Delta Rank with B : 2 vs 4

` See graph

` NOT SYNC'D

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

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

` See graph

` ---> RB-SYNC'D

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

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

` See graph

` ---> RB-SYNC'D

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

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

` See graph

` ---> RB-SYNC'D

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

Delta Rank with R : 3 vs 5
Delta Rank with B : 1 vs 4

` See graph

` NOT SYNC'D

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

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

` See graph

` ---> RB-SYNC'D

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

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

` See graph

` ---> RB-SYNC'D

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

Delta Rank with R : 4 vs 6
Delta Rank with B : 2 vs 5

` See graph

` NOT SYNC'D

SUMMARY

Graph Type
CC

ν(A)
2

ν(Δ)
2

π
[1, 2, 2, 3, 2, 2]

Dbly Stoch
false

SUMMARY
Graph Type		CC
ν(A)		2
ν(Δ)		2
π		[1, 2, 2, 3, 2, 2]
Dbly Stoch		false

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 18 9 32 32