Avoid Consecutive Games for Player in Round Robin
If a player is in the last match of a round, they should not be in the first match of the next round, so that they get a break like all other players.
An algorithm for six or more players: If both players from the last match of the last round are in the first and second matches of the next round, swap matches one and three of the round. Otherwise, if either player is in the first matches, swap matches one and two.
For five players, play the matches in the order AB CD - AE BC - DE AC - BD CE - AD BE.
For three or four players, it is impossible to avoid having players play matches in a row.
Ideally, for larger round robins, the length of the minimum break a player has would be maximised.