Greece and Rome in SGGK

I am fascinated by the Greek and Roman myths and histories and so I was intrigued by the references to Troy and Rome in Sir Gawain and the Green Knight. Maybe these comments were just to show Arthur's genealogy but I see some ways that the author could be comparing the history with Sir Gawain. In the Trojan War, the gods meddled with the direction of events, they chose certain people to be heroes and then sometimes caused the downfall of their own heroes, and there were many tests of various sorts for the heroes. In Sir Gawain, Morgan le Faye, who is a powerful magical being much like the Greek gods, decides to test the knights of King Arthur's court and sends Sir Gawain through a series of temptations. The Trojan War has lots of times when the hero has to do single combat with the enemy's hero or with a bad guy, and Sir Gawain has to face the Green Knight. The Greeks and Romans have many stories of women tempting men into giving up something, their power, their honor, their life... and Lady Bertilak tempts Sir Gawain into giving up his honor by accepting the green girdle. While many of these ideas are common themes in many stories from many different cultures, I think that the similarity to the Greek and Roman myths are significant because of the references to these stories at both the beginning and the end of Sir Gawain and the Green Knight.
Rachel Means