Question 2
Let $n$, $m$ be positive integers such that $n + m$ is odd. Assume that the edges of a complete bipartite graph $K_{n,m}$ are labeled by $1$ and $-1$ such that the sum of the numbers written on all edges is zero. Show that this graph has a spanning tree such that the sum of the numbers on its edges is $0$.
*A spanning tree is a sub-tree of the graph that contains all the vertices.*
*A spanning tree is a sub-tree of the graph that contains all the vertices.*