A school is preparing the schedule of classes for the next academic year. They are concerned about scheduling calculus, physics, English, statistics, economics, chemistry, and German classes, planning to offer a single section of each one. Below are the lists of courses that each of six students must take in order to successfully graduate. Determine the smallest number of class periods that can be used to schedule these courses if each student can take at most one course per class period. Explain why fewer class periods cannot be used.
| Student | Courses |
| 1 | Chemistry, Physics, Economics |
| 2 | English, German, Statistics |
| 3 | Statistics, Calculus, German |
| 4 | Chemistry, Physics |
| 5 | English, Chemistry |
| 6 | Chemistry, Economics |
Keller & Trotter, Applied Combinatorics, Graph Theory — Exercises, Exercise 16