The number before the graph is the length of shortest 3-cycle cover of the graph. 
Results for large instances are results of hands on analysis. They presence does not imply 
that I expect them to be solvable in reasonable time.

22
0:1,5,4
1:0,2,6
2:1,3,7
3:2,4,8
4:3,9,0
5:0,7,8
6:1,8,9
7:2,5,9
8:3,6,5
9:4,7,6

26
0:1,5,10
1:0,2,6
2:1,3,7
3:2,4,8
4:3,10,11
5:0,7,8
6:1,8,9
7:2,5,9
8:3,6,5
9:7,6,11
10:0,4,11
11:9,10,4

38
0:1,4,9
1:0,2,5
2:1,3,6
3:2,7,12
4:0,6,7
5:1,7,8
6:2,4,8
7:3,5,4
8:6,5,17
9:10,13,0
10:9,11,14
11:10,12,15
12:11,16,3
13:9,15,16
14:10,16,17
15:11,13,17
16:12,14,13
17:15,14,8

60
0:1,4,9
1:0,2,5
2:1,3,6
3:2,7,27
4:0,6,7
5:1,7,8
6:2,4,8
7:3,5,4
8:6,5,19
9:10,14,0
10:9,11,15
11:10,12,16
12:11,13,17
13:12,18,22
14:9,16,17
15:10,17,18
16:11,14,18
17:12,15,14
18:13,16,15
19:20,23,8
20:19,21,24
21:20,22,25
22:21,26,13
23:19,25,26
24:20,26,27
25:21,23,27
26:22,24,23
27:25,24,3

82
0:1,4,9
1:0,2,5
2:1,3,6
3:2,7,29
4:0,6,7
5:1,7,8
6:2,4,8
7:3,5,4
8:6,5,19
9:10,14,0
10:9,11,15
11:10,12,16
12:11,13,17
13:12,18,37
14:9,16,17
15:10,17,18
16:11,14,18
17:12,15,14
18:13,16,15
19:20,24,8
20:19,21,25
21:20,22,26
22:21,23,27
23:22,28,32
24:19,26,27
25:20,27,28
26:21,24,28
27:22,25,24
28:23,26,25
29:30,33,3
30:29,31,34
31:30,32,35
32:31,36,23
33:29,35,36
34:30,36,37
35:31,33,37
36:32,34,33
37:35,34,13

104
0:1,4,9
1:0,2,5
2:1,3,6
3:2,7,29
4:0,6,7
5:1,7,8
6:2,4,8
7:3,5,4
8:6,5,19
9:10,14,0
10:9,11,15
11:10,12,16
12:11,13,17
13:12,18,39
14:9,16,17
15:10,17,18
16:11,14,18
17:12,15,14
18:13,16,15
19:20,24,8
20:19,21,25
21:20,22,26
22:21,23,27
23:22,28,47
24:19,26,27
25:20,27,28
26:21,24,28
27:22,25,24
28:23,26,25
29:30,34,3
30:29,31,35
31:30,32,36
32:31,33,37
33:32,38,42
34:29,36,37
35:30,37,38
36:31,34,38
37:32,35,34
38:33,36,35
39:40,43,13
40:39,41,44
41:40,42,45
42:41,46,33
43:39,45,46
44:40,46,47
45:41,43,47
46:42,44,43
47:45,44,23

126
0:1,4,9
1:0,2,5
2:1,3,6
3:2,7,29
4:0,6,7
5:1,7,8
6:2,4,8
7:3,5,4
8:6,5,19
9:10,14,0
10:9,11,15
11:10,12,16
12:11,13,17
13:12,18,39
14:9,16,17
15:10,17,18
16:11,14,18
17:12,15,14
18:13,16,15
19:20,24,8
20:19,21,25
21:20,22,26
22:21,23,27
23:22,28,49
24:19,26,27
25:20,27,28
26:21,24,28
27:22,25,24
28:23,26,25
29:30,34,3
30:29,31,35
31:30,32,36
32:31,33,37
33:32,38,57
34:29,36,37
35:30,37,38
36:31,34,38
37:32,35,34
38:33,36,35
39:40,44,13
40:39,41,45
41:40,42,46
42:41,43,47
43:42,48,52
44:39,46,47
45:40,47,48
46:41,44,48
47:42,45,44
48:43,46,45
49:50,53,23
50:49,51,54
51:50,52,55
52:51,56,43
53:49,55,56
54:50,56,57
55:51,53,57
56:52,54,53
57:55,54,33

148
0:1,4,9
1:0,2,5
2:1,3,6
3:2,7,29
4:0,6,7
5:1,7,8
6:2,4,8
7:3,5,4
8:6,5,19
9:10,14,0
10:9,11,15
11:10,12,16
12:11,13,17
13:12,18,39
14:9,16,17
15:10,17,18
16:11,14,18
17:12,15,14
18:13,16,15
19:20,24,8
20:19,21,25
21:20,22,26
22:21,23,27
23:22,28,49
24:19,26,27
25:20,27,28
26:21,24,28
27:22,25,24
28:23,26,25
29:30,34,3
30:29,31,35
31:30,32,36
32:31,33,37
33:32,38,59
34:29,36,37
35:30,37,38
36:31,34,38
37:32,35,34
38:33,36,35
39:40,44,13
40:39,41,45
41:40,42,46
42:41,43,47
43:42,48,67
44:39,46,47
45:40,47,48
46:41,44,48
47:42,45,44
48:43,46,45
49:50,54,23
50:49,51,55
51:50,52,56
52:51,53,57
53:52,58,62
54:49,56,57
55:50,57,58
56:51,54,58
57:52,55,54
58:53,56,55
59:60,63,33
60:59,61,64
61:60,62,65
62:61,66,53
63:59,65,66
64:60,66,67
65:61,63,67
66:62,64,63
67:65,64,43

170
0:1,4,9
1:0,2,5
2:1,3,6
3:2,7,29
4:0,6,7
5:1,7,8
6:2,4,8
7:3,5,4
8:6,5,19
9:10,14,0
10:9,11,15
11:10,12,16
12:11,13,17
13:12,18,39
14:9,16,17
15:10,17,18
16:11,14,18
17:12,15,14
18:13,16,15
19:20,24,8
20:19,21,25
21:20,22,26
22:21,23,27
23:22,28,49
24:19,26,27
25:20,27,28
26:21,24,28
27:22,25,24
28:23,26,25
29:30,34,3
30:29,31,35
31:30,32,36
32:31,33,37
33:32,38,59
34:29,36,37
35:30,37,38
36:31,34,38
37:32,35,34
38:33,36,35
39:40,44,13
40:39,41,45
41:40,42,46
42:41,43,47
43:42,48,69
44:39,46,47
45:40,47,48
46:41,44,48
47:42,45,44
48:43,46,45
49:50,54,23
50:49,51,55
51:50,52,56
52:51,53,57
53:52,58,77
54:49,56,57
55:50,57,58
56:51,54,58
57:52,55,54
58:53,56,55
59:60,64,33
60:59,61,65
61:60,62,66
62:61,63,67
63:62,68,72
64:59,66,67
65:60,67,68
66:61,64,68
67:62,65,64
68:63,66,65
69:70,73,43
70:69,71,74
71:70,72,75
72:71,76,63
73:69,75,76
74:70,76,77
75:71,73,77
76:72,74,73
77:75,74,53