# hw6 - G Problem B Let τ G denote the number of spanning...

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MATH 145: HOMEWORK 6 ANDREW BERGET Solve problems 10.21, 10.22, 10.23, 10.28 (this is asking for unlabeled tress!), 10.30+, 10.31, 10.34+. Problem A.+ Let G be a graph and T is a spanning tree of G . Let f be an edge of G which is not an edge of T . (1) Prove that T f contains a unique cycle. (2) Prove that there there is always an edge f T such that T - e f is a spanning tree of
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Unformatted text preview: G . Problem B.+ Let τ ( G ) denote the number of spanning trees of G . For a non-loop edge e of G deﬁne the deletion of e from G , denoted G-e , and the contraction of G by e , denoted G/e . Prove that τ ( G ) = τ ( G-e ) + τ ( G/e ) . If this is hard for you, try and see why it is true for a small example. 1...
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