The main legal antecedents were a series of decisions that weakened the idea of separate but equal. These were cases like Sweatt v. Painter, Sipuel v. Board of Regents and Missouri ex rel Gaines v. Canada.
In these cases, the Supreme Court started to really hold states very strictly to the idea that separate accommodations for blacks and whites really had to be equal. This meant that states really had to provide schools (in these cases, law and graduate schools) for blacks that were equal. Otherwise, they had to allow blacks to go to "white" schools.
This line of cases set the stage for Brown v. Board of Education, where the Supreme Court said separate could never be equal.