Is there a resolution to the major conflict in "Killings"?If yes, what is it? If no, why?
In order to determine the conflict of a story, it is easiest to look at two things: the rising action and the climax. In a short story, the story line dictates that all events should lead to a climax which should come just before the resolution to the conflict. Though some might argue that the conflict of this story is the murder of Frank Fowler, according to the story line of this short story, it is more likely that the conflict is Matt Fowler's internal conflict in losing his son.
As such, the rising action of the story is the build up to the revenge murder of Strout. The climax is Strout's death. And the resolution is Matt Fowler's ability to go back to bed with his wife, having accomplished what he had been planning for so long. The irony here, of course, is that though this is Matt's chosen solution to his problem, is he really left with a sense of resolve? The story ends on this question, presented by his inability to embrace his wife. The audience is left with something to consider and decide for themselves.