If you restrict yourself to playing only matches involving two of the teams, then I can provide a potential solution. But there is a problem as the number of teams is odd, with one bye per round and only 8 rounds, 5 of the teams will never get a bye and end up playing one more match than the others.
If you start with the scedule below for 14 teams.
G1 G2 G3 G4 G5 G6 G7 G8
(A I) (H J) (G K) (F L) (E M) (C D) (B N)
(C N) (B I) (A J) (H K) (G L) (F M) (D E)
(E F) (D N) (C I) (B J) (A K) (H L) (G M)
(H M) (F G) (E N) (D I) (C J) (B K) (A L)
(B L) (A M) (G H) (F N) (E I) (D J) (C K)
(D K) (C L) (B M) (H A) (G N) (F I) (E J)
(E K) (D L) (C M) (A B) (H N) (G I) (F J)
(G J) (F K) (E L) (D M) (B C) (A N) (H I)
Now delete all matches involving team K and you have a schedule where no two teams are matched together more than once and 12 out of 13 teams play each game. You could add in two more rounds to make sure everyone plays every game, but it will not be pretty. Things would be much better if you could find a 14th team.
Ian.
