Unformatted text preview: G , and let φ : E ( G ) → IR + be an s-t Fow. Show that there is an s-t Fow ψ : E ( G ) → ZZ + so that (a) its value is at least that of φ , and (b) | ψ ( e )-φ ( e ) | < 1 for every edge e of G . 4. Let T be a tree. Show that T has a perfect matching if and only if for every vertex v , exactly one of the components of T \ v has an odd number of vertices. [Hint for “if”: use induction on | V ( T ) | , ±nd a leaf with a neighbour of degree 2, and delete them both.] 1...
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- Spring '10
- Logic, Trigraph, Bipartite graph, distinct vertices, T \v, CSORE4010— HOMEWORK