Question 3.115

85. The legislature of a city has committees devoted to the following governmental areas:

; ; ; ; ; ; , . To schedule meetings for these committees in as few time slots as possible, consider the graph model below.

image
  1. Complete the entries in the table below that would display the “conflict” information represented by the graph, where an X indicates two committees that cannot meet at the same time because they have at least one common member.
  2. What is the minimum number of time slots in which it is possible to schedule these committees?
  3. If there are only three rooms with the audio and video setups needed for the committees to meet, what is the minimum number of time slots during which the committees can meet?

85.

(a) Drawings can

image

(b) 2

(c) 3 (Two rooms will be used for three committee meetings and one room for two committee meetings.)