close, closely fought, equal, even | one-sided, unequal
The contest was too one-sided to be exciting.

open
This contest is wide open: any of half a dozen teams could win it.

fair
The other bidders for the contract complained that it had not been a fair contest.

exciting, good, great, thrilling | bitter | head-to-head
The contestants are eliminated one by one until the last two compete in a head-to-head contest.

global, international, local, national, regional | election/electoral, gubernatorial, leadership, political, presidential | beauty, song, sporting, talent

have, hold, run
We have three major beauty contests a year. | Sporting contests are held in the arena.

compete in, enter, take part in
A third candidate has entered the contest for the Republican nomination.

win, lose

take place

during a/the ~
During the election contest newspapers are not allowed to publish public opinion polls.

in a/the ~
Both sides are predicting victory in this close contest.

out of a/the ~
Jackson has injured his knee and is now out of the contest.

~ against
They won the doubles contest against the Williams sisters.

~ between
the contest between these two great boxers

~ for
the contest for the leadership of the party

~ over
In the animal kingdom intruders usually lose contests over territories.

~ with
The New Zealanders are looking forward to future contests with South Africa.

be no contest
(= used when one side in a contest is much stronger than the other and is sure to win),

the winner of a contest

bitterly, fiercely, hotly, keenly
The election was bitterly contested.

successfully, unsuccessfully

fiercely, hotly, strongly, vigorously
His views on evolution are strongly contested by other scientists.

successfully, unsuccessfully
Defence lawyers successfully contested the case.