League and round-robin fixtures for 6 teams

Week 1 Week 2 Week 3 Week 4 Week 5
 1v 6  5v 1  1v 4  3v 1  1v 2
 2v 5  4v 2  2v 3  6v 2  5v 3
 3v 4  6v 3  5v 6  4v 5  4v 6

 

In the above fixtures the following teams are paired so when one is at home the other is away:

1 and 6
2 and 4
3 and 5