Why does the play open with a mention of the tragedy of Oedipus?
The play opens with the mention of the Oedipal tragedy in order to situate Antigone's experience in the larger context of the family history. Audiences in Sophocles' time would be familiar with the Oedipus story, and immediately connect the conflict in this third play of the trilogy (which was actually written first).
Placing the events in the context of the entire Oedipal tragedy establishes Antigone in the Greek tragic tradition, as well as reminding the audience of the catharsis they experienced at the end of the first two plays. It also serves to extend the curse upon the house of Oedipus, which connects to the ideas of both free will and fate. It essentially considers the concept of the sins of the parents being visited upon the children. Also, it heightens the tragedy of Antigone, Creon, Hamon, & Ismene, in that they are the only remaining members of this family. Each death becomes yet another blow to the already reeling relatives.
Finally, the mention of Oedipus may serve as Sophocles' warning to the historical leader Pericles, cautioning against authoritarian rule. This also connects to the character of Creon in Antigone, suggesting that Sophocles wanted to establish a pattern of destruction amongst leaders who rule inflexibly.