Question: 1. List at least two criteria that (when present) prevent a tree from having a perfect matching.
2. Does every bipartite graph have a perfect matching?
3. What is the relationship between the number of edges in a matching and the number of vertices in that matching?
4. Is it possible for a graph with an odd number of vertices to have a matching?
5. Is it possible for a graph with an odd number of vertices to have a perfect matching?