The key to understanding the relationship between Creon and Oedipus is also the reason why the title of Sophocles' play should be translated as "Oedipus the Tyrant" rather than "Oedipus Rex" (Latin for "Oedipus the King").
In classical Greek, "Oedipus Turannos" (sometimes Latinized as "Tyrannus") means "Oedipus the Tyrant". A tyrant in Greek can be a bad ruler, but is not necessarily so. The distinction between a king and a tyrant is simply that a king is a monarch or autocrat (sole ruler) who rules by virtue of some legitimate process of succession such as heredity (e.g. the son of the previous king). A tyrant is a ruler who comes to power without some official form of legitimacy, sometimes as a result of a military coup but often in archaic Greece by popular acclaim; many historians consider tyranny a transitional phase between hereditary monarchy and democracy in Greece.
Oedipus is functioning as a tyrant in Thebes, a popularly acclaimed leader. Creon, as the brother of Laius, actually has (according to the information we have at the beginning of the play), a better claim on the throne than Oedipus. Thus Oedipus is worried about Creon attempting to usurp his power. Tiresias, as a prophet, is also part of the established, legitimate power structure, and Oedipus is worried that he is a pawn of Creon. Creon reassures Oedipus repeatedly that he has no desire for the crown, and simply wants to do what is best for Thebes.
Ironically, it is at the end of the play, when we discover that Oedipus is the son of Laius, that he becomes the legitimate king of Thebes just as he renounces his power as tyrant.
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