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List at least two criteria that when present prevent a tree

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?

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Mathematics: List at least two criteria that when present prevent a tree

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