I don't believe an actual rose is ever mentioned specifically in William Faulkner's classic short story, "A Rose for Emily." The color of a rose is referred to twice in the final paragraphs, however.
A thin, acrid pall as of the tomb seemed to lie everywhere upon this room decked and furnished as for a bridal: upon the valance curtains of faded rose color. upon the rose-shaded lights, upon the dressing table...
I believe the use of the word "rose"--universally a symbol of love--is used to symbolically illustrate the lost love that Miss Emily lived with for so long. She was a woman so desirous of love and so unable to show it. The title also seems to be a kind of final salute to Emily, a symbol of flowers for a funeral, perhaps; a need for the sweet smell of the flower in a house filled with the stench of death; or possibly even a suggestion of the various stages of blooming that the flower goes through. In the end, we find that Emily has preserved Homer's body even as it turns to dust, not unlike the manner in which a person who has received a rose preserves it for posterity.
There is no actual rose (as in a flower) in the story, although many of the things found in Miss Emily's room after she dies are rose colored.
I believe that the rose that the title refers to is actually Homer Barron, or at least his body. His body has been kept in her room, all dried up and withered, just like a rose that someone would keep as a souvenir of some old dance or something like that.
So, I think that the rose of the title is actually him and that the title is meant to show how she had this one bit of life, thirty years ago, and has been holding on to the memory ever since.
A rose is never mentioned in the story. It is one of the ambiguous titles that has baffled Faulkner scholars for many years. Most consider it to be Faulkner's appreciation to Emily that the character did live, just not very well. It is analogous to giving someone a bouquet of roses for a job well done. Since she didn't lead a very full life and was seen in the story as "stuck in time," she at least deserves one rose for attempting to find a certain dignity in her life, though it turned out not to her liking. Most teachers probably do not understand its significance.