Use backtracking with states (bitmask, degrees) where bitmask represents the set of courses, if the ith bit is 1 then the ith course was taken, otherwise, you can take the ith course. Degrees represent the degree for each course (nodes in the graph).

Note that you can only take nodes (courses) with degree = 0 and it is optimal at every step in the backtracking take the maximum number of courses limited by k.