Fate is a theme that often occurs in Greek writing, tragedies in particular. The idea that attempting to avoid an oracle is the very thing which brings it about is a common motif in many Greek myths, and similarities to Oedipus can for example be seen in the myth of the birth of Perseus.
Two oracles in particular dominate the plot of Oedipus the King. In lines 711 to 714, Jocasta relates the prophecy that was told to Laius before the birth of Oedipus. Namely:
(The oracle) told him
that it was his fate that he should die a victim
at the hands of his own son, a son to be born
of Laius and me.

The oracle told to Laius tells only of the patricide; the incest is missing. Prompted by Jocasta's recollection, Oedipus reveals the prophecy which caused him to leave Corinth (791-93):
that I was fated to lie with my mother,
and show to daylight an accursed breed
which men would not endure, and I was doomed
to be murderer of the father that begot me.

The implication of Laius's oracle is ambiguous. A prominent school of thought argues that the presentation of Laius's oracle in this play differs from that found in (e.g.) Aeschylus's Oedipus trilogy produced in 467 BC.

Sophocles had the option of making the oracle to Laius conditional (if Laius has a son,
that son will kill him) or unconditional (Laius will have a son who will kill him). Both
Aeschylus and Euripides write plays in which the oracle is conditional; Sophocles...
chooses to make Laius's oracle unconditional and thus removes culpability for his sins
from Oedipus, for he could not have done other than what he did, no matter what action he took.