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Find a way to color the vertices using only three colors

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Reference no: EM131574424

Question: In this exercise a graph is used to help solve a scheduling problem. Twelve faculty members in a mathematics department serve on the following committees:

- Undergraduate Education: Tenner, Peterson, Kashina, Cohen

- Graduate Education: Gatto, Yang, Cohen, Catoiu

- Colloquium: Sahin, McMurry, Ash

- Library: Cortzen, Tenner, Sahin

- Hiring: Gatto, McMurry, Yang, Peterson

- Personnel: Yang, Wang, Cortzen

The committees must all meet during the first week of classes, but there are only three time slots available. Find a schedule that will allow all faculty members to attend the meetings of all committees on which they serve. To do this, represent each committee as the vertex of a graph, and draw an edge between two vertices if the two committees have a common member. Find a way to color the vertices using only three colors so that no two committees have the same color, and explain how to use the result to schedule the meetings.

Reference no: EM131574424

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