What Is the Minimum Number of Meeting Times Needed for Overlapping Committees?

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SUMMARY

The minimum number of meeting times required to ensure that no committee members are scheduled for overlapping meetings is determined by analyzing the membership of the six committees: C1, C2, C3, C4, C5, and C6. Each committee has specific members, leading to potential conflicts. By applying graph theory principles, it is established that at least four distinct meeting times are necessary to accommodate all members without overlap.

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  • Understanding of set theory and its application in committee membership
  • Familiarity with graph theory concepts, particularly bipartite graphs
  • Basic knowledge of combinatorial optimization
  • Experience with problem-solving in scheduling and resource allocation
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  • Research graph theory applications in scheduling problems
  • Learn about bipartite graphs and their properties
  • Explore combinatorial optimization techniques for resource allocation
  • Investigate algorithms for solving the minimum coloring problem in graphs
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This discussion is beneficial for computer scientists, operations researchers, and anyone involved in scheduling and resource management within organizations.

johndunlop
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The computer science department has 6 committees that meet once a month. How many different meeting times (in a month) must be used to guarantee that no one is scheduled to be at 2 meetings at the same time, if committees and their members are given below.

C1 = {Daim, Viknesh, Lila}, C2 = {Viknesh, Johanes, Philo}, C3 = {Daim, Lila, Philo},
C4 = {Johanes, Lila, Philo}, C5 = {Daim, Lila}, C6 = {Viknesh, Daim, Philo}
 
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Hello johndunlop and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

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