Please don't hand write. Thanks!

[15 pts] The complete bipartite graph Km,n where m, n 2 1, has m red nodes, n blue nodes and has an edge between every red node and every blue node. There are no edges between nodes of the same color. For illustration, here is K3,2: B B R R R (a) Let D be the number of edges of Km,, that we have to delete from the graph to obtain a spanning tree. Prove that D is divisible by m - 1. (b) Assume that m > n. Prove that the length of a longest path in K'm,n is even