Exercise
Consider the permutation group G = < a, b> where a = (1,2)(3,4) and b = (1,3)(2,4). The action of both a and b is fully described by the picture:
How many Schreier trees with root 1 for {a, b} are there?
1
2
4
No. How many trees are on all 4 vertices?
No. How many trees are on all 4 vertices?
Yes.
Deletion of an edge always results in a Schreier tree.