mixed doubles tennis round robin for 20 players

[tennisnut]

I need a format for a mixed doubles tennis round robin for 20 players (10 men and 10 women)where each man pairs with each women once and against each other once.

[Ian Wakeling]

With mixed doubles there is a problem.  Everyone has 10 possible partners and 10 possible opposite sex opponents, but only 9 possible same sex opponents.  A common solution is to go for 9 games each, forbidding one specific opposite sex pairing per player. Usually this is presented as a schedule for 10 husbands (H) and 10 wives(W), with a spouse avoidance property, however it can of course be used for any group of 10 men and 10 women.

There is an additional problem when there are 20 mixed doubles players. While it's possible to list all the games required:

(H1 W3 v H2 W6) (H1 W9 v H3 W8) (H1 W7 v H4 W5) (H1 W0 v H5 W3) (H1 W8 v H6 W0)
(H1 W2 v H7 W4) (H1 W6 v H8 W7) (H1 W5 v H9 W2) (H1 W4 v H0 W9) (H2 W4 v H3 W7)
(H2 W1 v H4 W9) (H2 W8 v H5 W6) (H2 W0 v H6 W4) (H2 W9 v H7 W0) (H2 W3 v H8 W5)
(H2 W7 v H9 W8) (H2 W5 v H0 W1) (H3 W5 v H4 W8) (H3 W2 v H5 W1) (H3 W9 v H6 W7)
(H3 W0 v H7 W5) (H3 W1 v H8 W0) (H3 W4 v H9 W6) (H3 W6 v H0 W2) (H4 W6 v H5 W9)
(H4 W3 v H6 W2) (H4 W1 v H7 W8) (H4 W0 v H8 W6) (H4 W2 v H9 W0) (H4 W7 v H0 W3)
(H5 W7 v H6 W1) (H5 W4 v H7 W3) (H5 W2 v H8 W9) (H5 W0 v H9 W7) (H5 W8 v H0 W4)
(H6 W8 v H7 W2) (H6 W5 v H8 W4) (H6 W3 v H9 W1) (H6 W9 v H0 W5) (H7 W9 v H8 W3)
(H7 W6 v H9 W5) (H7 W1 v H0 W6) (H8 W1 v H9 W4) (H8 W2 v H0 W7) (H9 W3 v H0 W8)

there is no known way of arranging them into 9 rounds of 5 matches each, where each player plays exactly once per round.  If this is what you were looking for then it may be possible for you to rearrange the games above so you have rounds of three or four games each.

[tennisnut]

Thank you for your help.  There are no husbands and wives playing.  We were hoping to find a format where every woman partners with every man once.  We plan on playing 4-game sets.  Everyone serves once.  Is there a format where we can play 10 rounds??

Thank you,  Tennisnut

[bburwitz]

Did you ever find a schudule for 20 players?  I'm looking for the same thing? There has to be a way of a least matching all the males with each female once, which would make 10 rounds of play!  It might not be perfectly balanced, but I'm sure there is a way?  

[Ian Wakeling]

In the schedule below all 100 mixed doubles partnerships occur exactly once.  The opponents are not perfectly balanced,  most players will have about two or three players whom they never oppose and about three or four players with whom they oppose twice.  Would you consider using it?

[(M04 F04):(M09 F08)] [(M02 F02):(M05 F06)] [(M01 F01):(M03 F10)] [(M10 F03):(M08 F05)] [(M07 F09):(M06 F07)]
[(M04 F03):(M07 F02)] [(M08 F01):(M06 F05)] [(M09 F07):(M05 F10)] [(M02 F04):(M01 F06)] [(M10 F09):(M03 F08)]
[(M04 F10):(M01 F09)] [(M09 F02):(M08 F08)] [(M02 F05):(M03 F07)] [(M06 F03):(M10 F04)] [(M05 F01):(M07 F06)]
[(M09 F10):(M06 F02)] [(M07 F03):(M01 F05)] [(M04 F01):(M08 F07)] [(M02 F06):(M10 F08)] [(M05 F09):(M03 F04)]
[(M06 F06):(M04 F07)] [(M07 F04):(M10 F02)] [(M05 F08):(M01 F10)] [(M02 F01):(M09 F05)] [(M03 F09):(M08 F03)]
[(M07 F10):(M08 F06)] [(M01 F04):(M03 F01)] [(M09 F09):(M10 F05)] [(M06 F08):(M05 F07)] [(M04 F02):(M02 F03)]
[(M07 F07):(M02 F09)] [(M08 F02):(M01 F08)] [(M03 F06):(M09 F04)] [(M06 F10):(M04 F05)] [(M05 F03):(M10 F01)]
[(M02 F10):(M03 F03)] [(M07 F08):(M06 F04)] [(M01 F02):(M10 F07)] [(M08 F09):(M09 F01)] [(M04 F06):(M05 F05)]
[(M06 F09):(M05 F02)] [(M07 F01):(M10 F10)] [(M03 F05):(M04 F08)] [(M01 F03):(M09 F06)] [(M08 F04):(M02 F07)]
[(M04 F09):(M10 F06)] [(M05 F04):(M08 F10)] [(M01 F07):(M09 F03)] [(M02 F08):(M06 F01)] [(M03 F02):(M07 F05)]

[bburwitz]

Thank you for allyour help.  This is exactly what I am looking for.  I know its not perfect, but at least everyone gets partnered together.

[kenbrockway]

This only uses 8 men 9 times and 9 men once?

[Ian Wakeling]

I am not certain that I understand your question, can you give more details please.  The first schedule above is for 10 men, M01 to M10, and they should play once in every round (row).