5) The register at Paltry University is creating its exam schedule. It needs to create exam one final exam slot for each

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5 The Register At Paltry University Is Creating Its Exam Schedule It Needs To Create Exam One Final Exam Slot For Each 1 (131.03 KiB) Viewed 58 times

5) The register at Paltry University is creating its exam schedule. It needs to create exam one final exam slot for each course in such a way that no conflicts occur for students. The university has the following potential conflicts. i. Anthropology and Biology have a common student. ii. Anthropology and Computer Science have a common student. iii. Anthropology and Dance have a common student. iv. Anthropology and Geology have a common student. v. Biology and Computer Science have a common student. vi. Biology and Dance have a common student. vii. Biology and Environmental Science have a common student. viii. Biology and Geology have a common student. ix. Computer Science and Dance have a common student. x. Computer Science and French have a common student. xi. Computer Science and Geology have a common student. xii. Dance and Environmental Science have a common student. xiii. Dance and French have a common student. xiv. Environmental Science and Geology have a common student. xv. French and Geology have a common student. Given this information, (a) Draw a graph such that the chromatic number of the graph determines the fewest number of possible final exam slots that make the scheduling possible. (b) Determine the fewest number of exam slots needed. (c) If a single course can be chosen to not need a a final exam, is it possible to reduce the number of exam slots necessary?