How to plan fixtures for a soccer league? I want to generate fixtures for a league tournament. This is all I have so far:
WEEK 1

team0 vs team1
team2 vs team3
team4 vs team5
team6 vs team7
team8 vs team9

WEEK 2

team2 vs team0
    
WEEK 3

team0 vs team3
    
WEEK 4

team4 vs team0
    
WEEK 5

team0 vs team5
    
WEEK 6

team6 vs team0
    
WEEK 7

team0 vs team7
    
WEEK 8

team8 vs team0
    
WEEK 9

team0 vs team9

as you may see I have only team0 fixtures for all 9 weeks. How can I generate the remaining fixtures from there? I have found some generators online but these only can generate the fixtures randomly and I need them to part from this specific order.
Thank you.
 A: This is a well-known problem of edge-colouring a complete graph $K_{n}$ with $n-1$ (or $n$) colours.
It has an elegant solution:


Soifer (2008) provides the following geometric construction of a coloring in this case: place $n$ points at the vertices and center of a regular $(n − 1)$-sided polygon. For each color class, include one edge from the center to one of the polygon vertices, and all of the perpendicular edges connecting pairs of polygon vertices.

Wikipedia,
After you did the colouring, let pairs connected with red colour play in week 1, pairs with blue colour in week 2 and so on.
A: I started with a random arrangement I found online. Then, I rearranged the labels of the teams to make sure the week 1 matchups were what you wanted. Then, I also had to rearrange the labeling of the weeks after the first week to have team 0 play team k in week k.
Week opponents
1  0  1
1  2  3
1  4  5
1  6  7
1  8  9
2  0  2
2  4  1
2  6  3
2  8  5
2  9  7
3  0  3
3  1  5
3  2  7
3  4  9
3  6  8
4  0  4
4  6  2
4  8  1
4  9  3
4  7  5
5  0  5
5  3  7
5  1  9
5  2  8
5  4  6
6  0  6
6  8  4
6  9  2
6  7  1
6  5  3
7  0  7
7  5  9
7  3  8
7  1  6
7  2  4
8  0  8
8  9  6
8  7  4
8  5  2
8  3  1
9  0  9
9  7  8
9  5  6
9  3  4
9  1  2
