How would you characterize Emily and her father's relationship?

Emily and her father have a very strange and strangled relationship.  In the story, Faulkner mentions how "the Griersons held themselves a little too high for what they really were," thus "None of the young men were quite good enough for Miss Emily and such."  He had such a stranglehold on Miss Emily that she never in fact married, though the closest she came was in being courted by Homer Barron.  However, that courtship came...

Emily and her father have a very strange and strangled relationship.  In the story, Faulkner mentions how "the Griersons held themselves a little too high for what they really were," thus "None of the young men were quite good enough for Miss Emily and such."  He had such a stranglehold on Miss Emily that she never in fact married, though the closest she came was in being courted by Homer Barron.  However, that courtship came after her father's death.  Homer would not have been the type of man that Miss Emily's father would have approved of because he was "a Yankee--a big, dark, ready man, with a big voice and eyes lighter than his face."  The people in the town even comment, "'Of course a Grierson would not think seriously of a Northerner, a day laborer.'"  When Homer disappears later in the story, the reader believes that Miss Emily has dismissed him.

However, while Miss Emily's father may have been overbearing, she also had this strange connection to him.  When he dies, "She told them [the ladies calling] that her father was not dead.  She did that for three days, with the minsters calling on her, and the doctors, trying to persuade her to let them dispose of the body."  Without her father in her life, Miss Emily did not know how to behave because he had controlled every aspect of her life.  This same scene is repeated with Homer Barron.  When there are rumors that he is going to leave Miss Emily instead of marrying her, she poisons him with arsenic and lays him out in an upstairs bedroom:

The body had apparently once lain in the attitude of an embrace, but now the long sleep that outlasts love, that conquers even the grimace of love, had cuckolded him.  What was left of him, rotted beneath what was left of the nightshirt, had become inextricable from the bed in which he lay...

Emily decides to keep Homer in her clutches, in a way that she could not with her father.