3. Let G be the bipartite graph below, and let M = {v₁W₁, V3W3, V4w4} be the match- ing in G shown with bold (red) edges. (a) Grow a maximal alternating tree in G with respect to M with root v2. (b) Use this tree to obtain a matching in G with four edges. [3 marks] [2 marks] (c) Is it possible to find an augmenting path with respect to this new matching? If so, give such a path by growing a maximal alternating tree, and then augment along this path to obtain a matching with five edges. Otherwise give reasons why such an augmenting path does not exist. [3 marks]

Fig: 1