Unformatted text preview: G , and let φ : E ( G ) → IR + be an st Fow. Show that there is an st 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
 chudnovsky
 Logic, Trigraph, Bipartite graph, distinct vertices, T \v, CSORE4010— HOMEWORK

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