A red match was one of the two types of matches in Tsunkatse.
In a red match, the fight continued until one opponent killed the other. This was opposed to the other type of Tsunkatse match, the blue match, in which a fighter was merely required to knock out his or her opponent or otherwise cause so much pain to the opponent that he or she was unwilling to continue.
In 2376, Seven of Nine engaged in a red match with a Hirogen fighter. The match was ended prematurely when both fighters were beamed aboard the USS Voyager. (VOY: "Tsunkatse")