Let u be any minimizer in the tutte-berge formula. let v1; ; vk be the connected components of g u. show that, for any maximum matching m, we must have that (a) m contains exactly bjvi j =2c edges from g [vi ] (the subgraph of g induced by the vertices in vi), i. e., g [vi ] is perfectly matched for the even components vi and near-perfectly matched for the odd components. (b) each vertex u 2 u is matched to a vertex v in an odd component vi of g u. (c) the only unmatched vertices must be in odd components of g