Who is Manuel Cardoso, and Carmen Silveira- The Other Duel from Collected Fictions and what is their importance?

Manuel and Carmen are neighbors. They are ranch owners, and they are competing for the love of the same woman. Over the course of the story, Silveira comes to the conclusion that Carmen has poisoned his dog. When the two men are captured, they have a race, after their throats are cut, dying in the act.