Given a list of $N$ courses, $M$ students, the list of courses each student is taking and an integer $K$ representing the duration of the exam phase, is there an exam schedule consisting of $K$ dates so that there are no conflicts? Can you show that this problem is as difficult as the Clique-Cover problem (is $NP$-complete)?
2026-03-25 20:36:05.1774470965
Find an assignment of courses to days so that no student has more than one exam on the same day is NP-complete?
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Let the courses be vertices. Draw an edge between two if those courses have no student in common, i.e. their exams may be scheduled concurrently. If there happens to be a $3$-clique, then all $3$ of those courses may have their exams at the same time.