I need help on this question. Please provide the solution with explaination. Thank you!

Let G be be a graph where each edge is colored and multiple edges can share the same color. We are given three distinct nodes v_1, v_2 and v_3 (the graph could have many nodes).The graph is good if there is an infinite walk from v_1 that passes v_2 for only finitely many times and passes v_3 for infinitely many times and, after certain point on the walk, the walk only contains either red degs or green edges. Design an algorithm that decides whether a graph is good. Let G be be a graph where each edge is colored and multiple edges can share the same color. We are given three distinct nodes v_1, v_2 and v_3 (the graph could have many nodes).The graph is good if there is an infinite walk from v_1 that passes v_2 for only finitely many times and passes v_3 for infinitely many times and, after certain point on the walk, the walk only contains either red degs or green edges. Design an algorithm that decides whether a graph is good