User blog:Wythagoras/Minor(2)

I hope I didn't mess up anything again.

K1,n graphs
With the graphs K1,n we can create a sequence just as we did with n-paths. If we have two K1,n+1 graphs, we can create an sequence with length \(f_{\omega}(n)\) (or maybe longer). This is not allowed in SCG, but it is in Minor.

Minor(2) sequence
The sequence starts at graph 3.

03. 3-path

04. A square with two diagonals

05. A square with one diagonal and a dot

06. A square with one diagonal

07. A square and a triangle

08. A square and K1,3

09. A square and two sticks and a dot

10. A square and two sticks

11. A square and a stick and 5 dots

16. A square and a stick

17. A square and 11 dots

28. A square

29. 7 triangles with a dot in the middle connected and a dot

30. 7 triangles with a dot in the middle connected

31. 6 triangles with a dot in the middle connected and two triangles and a dot

32. 6 triangles with a dot in the middle connected and two triangles

33. 6 triangles with a dot in the middle connected and a triangle and K1,5

34. 6 triangles with a dot in the middle connected and a triangle and K1,4 and a stick

35. 6 triangles with a dot in the middle connected and a triangle and K1,4 and 3 dots

38. 6 triangles with a dot in the middle connected and a triangle and K1,4

39. 6 triangles with a dot in the middle connected and a triangle and 3 K1,3s

40. 6 triangles with a dot in the middle connected and a triangle and 2 K1,3s and 2 sticks and a dot

41. 6 triangles with a dot in the middle connected and a triangle and 2 K1,3s and 2 sticks

42. 6 triangles with a dot in the middle connected and a triangle and 2 K1,3s and 1 stick and 5 dots

47. 6 triangles with a dot in the middle connected and a triangle and 2 K1,3s and 1 stick

48. 6 triangles with a dot in the middle connected and a triangle and 2 K1,3s and 11 dots

59. 6 triangles with a dot in the middle connected and a triangle and 2 K1,3s

60. 6 triangles with a dot in the middle connected and a triangle and K1,3 and 14 sticks and a dot

61. 6 triangles with a dot in the middle connected and a triangle and K1,3 and 14 sticks

...

\(>f_{\omega}(1000)\). 6 triangles with a dot in the middle connected

one later. 5 triangles with a dot in the middle connected and \(f_{\omega}(1000)\) triangles

\(>f_{\omega+1}(f_{\omega}(1000))\). 5 triangles with a dot in the middle connected

\(>f_{\omega+1}^2(f_{\omega}(1000))\). 4 triangles with a dot in the middle connected

\(>f_{\omega+1}^3(f_{\omega}(1000))\). 3 triangles with a dot in the middle connected

\(>f_{\omega+1}^4(f_{\omega}(1000))\). 2 triangles with a dot in the middle connected

\(>f_{\omega+1}^5(f_{\omega}(1000))\). a triangle with a dot in the middle connected

A bound for Minor(2): \(>f_{\omega+1}^6(f_{\omega}(1000))\), but I guess this is very weak.