Full solution for only (C), thank you!

[10] 1. Bipartite Graphs and Beyond. Consider the following graph: [4] (a) Is it bipartite or not? Justify your claim. (2) (b) Suppose the edge e = {0,P} was added. Would your answer change? [4] (c) Let's generalize the colouring procedure from tutorial 3 to determine if a graph G is tripartite a graph in which we can assign one of three colours to all vertices such that no edge has endpoints with the same colour. Starting any vertex of G, we will run BFS and assign: the colour red to all vertices at level 3k, the colour blue to all vertices at a level 3k + 1, the colour green to all vertices at a level 3k + 2. We then test for tripartiteness by checking if any edge has endpoints of the same colour. Either prove or disprove the correctness of this procedure to determine if G is tripartite