Trees are the focus of this problem.
(a) Draw a tree that has nine vertices, and label the vertices.
(b) Redraw the tree so that it is clear that the tree is bipartite.
(c) Mark the bipartitely drawn tree so that it is a tree with eight vertices connected to a tree with one vertex.
(d) Mark (another copy of) the bipartitely drawn tree so that it is a tree with five vertices connected to a tree with four vertices.
(e) Show by induction that every tree is bipartite.