For each of the ff questions, either choose True or False and provide an explanation.

1. Let M be matching in a graph G, and let B be a blossom w/r/t G with 2k +1 edges. Let G' = G/B be the graph obtained by contracting B. Let M be a maximum matching in G'. Then the matching M'' in G that adds k edges B to M' is a maximum cardinality matching. T/F

2. Suppose that the capacities of the edges of an st network are integers that are all evenly divisible by 3. (E.g., 3, 6, 9, 12, etc.) Then there exists a maximum flow, such that the flow on each edge is also evenly divisible by 3. T/F