2. Let G be a graph with a designated start node and designated end node. Each node in G has a color. A walk on the graph may contain loops. Prove that there is an algorithm to decide whether there is a walk on the G that starts with the start node and ends with the end node and on which both of the following are true: (a) the number of reds nodes is greater than the number of green nodes; (b) the walk contains at least 5 blue nodes but no more than 3 yellow nodes 2. Let G be a graph with a designated start node and designated end node. Each node in G has a color. A walk on the graph may contain loops. Prove that there is an algorithm to decide whether there is a walk on the G that starts with the start node and ends with the end node and on which both of the following are true: (a) the number of reds nodes is greater than the number of green nodes; (b) the walk contains at least 5 blue nodes but no more than 3 yellow nodes