Question 3.125

95. Each vertex in the graph below represents a child who attends a daycare center. An edge between two children indicates these children tend to cause problems when they are in the same play group. What is the minimum number of play groups that will ensure that no conflicts arise? Can conflict-free play groups with the same number of children in each group be formed?

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95.

Three play groups will ensure no conflict. Four equalsize conflict-free groups can be formed. These groups would have size 2.