Bye (noun)

1. A match or contest in a tournament in which a player or team advances to the next round without playing.
2. A farewell remark or gesture.
3. A position in a tournament or competition in which a player or team advances to the next round without playing.

Origin:

Middle english by, from old english bī; akin to old high german bī by, latin ambi- around, greek amphi both ways.

Examples:

1. They received a bye in the first round.
2. She said bye to her friends before leaving.
3. The team had a bye in the first round of the tournament.
4. He got a bye in the first round of the competition.
5. She said bye to her family before going on a trip.