In this exercise a graph is used to help solve a scheduling problem. Twelve faculty members in a mathematics department serve on the followingcommittees:Undergraduate Education: Tenner, Peterson,Kashina, DegrasGraduate Education: Hu, Ramsey, Degras, BergenColloquium: Carroll, Drupieski, Au-YeungLibrary: Ugarcovici, Tenner, CarrollHiring: Hu, Drupieski, Ramsey, PetersonPersonnel: Ramsey, Wang, UgarcoviciThe 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 facultymembers to attend the meetings of all committees on which they serve. To do this, represent each committee as the vertex of a graph, and drawan 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.
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, Degras
Graduate Education: Hu, Ramsey, Degras, Bergen
Colloquium: Carroll, Drupieski, Au-Yeung
Library: Ugarcovici, Tenner, Carroll
Hiring: Hu, Drupieski, Ramsey, Peterson
Personnel: Ramsey, Wang, Ugarcovici
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.
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