Consider a setup where we want to separate the nodes into groups such that no two nodes that are adjacent are in the same group. For example, see Figure 3, where both graphs on the left and right can be separated into three groups each (let them be the red, blue, green groups). Answer the following questions. Figure 3: Two examples of graphs where the nodes can be partitioned into 3 groups 3 3 each. Cr 5 Removing a node from a graph may or may not decrease the number of groups you can build this way. For example, removing any node in the graph on the left in Figure 3 will lead to a decrease in the number of groups (from 3 to 2) whereas removing nodes 4 or 5 in the graph on the right will not decrease the number of groups (it is still 3 even after that removal). Write a mathematical formulation to identify the k nodes you should remove to decrease the number of groups you can build