6.042 at MIT is often taught using recitations. Suppose it happened that 8 recitations were needed, with two or three staff members running each recitation. The assignment of staff to recitation sections, using their secret code names, is as follows: - R1: Maverick, Goose, Iceman - R2: Maverick, Stinger, Viper - R3: Goose, Merlin - R4: Slider, Stinger, Cougar - R5: Slider, Jester, Viper - R6: Jester, Merlin - R7: Jester, Stinger - R8: Goose, Merlin, Viper Two recitations can not be held in the same 90-minute time slot if some staff member is assigned to both recitations. The problem is to determine the minimum number of time slots required to complete all the recitations. (a) Recast (translate) this problem as a question about coloring the vertices of a particular graph. (b) Draw the graph and explain what the vertices, edges, and colors represent. (One free flowchart building application that will work to make such an image is draw.id. If you have a goal of becoming a serious LaTeX nerd, try out the tikz package that is already loaded for this document.) (c) Show a coloring of this graph using the fewest possible colors; prove why no fewer colors will work. (d) What is the resulting schedule of recitations implied by the coloring