Competition problem — Combinatorics

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Combinatorics Difficulty 5.8 AIME, harder Prove it

12. ${ }^{+}$ Prove: Given $k \in \mathbb{N}$ and an edge $e$ in a graph $G$ , there are only finitely many cuts in $G$ that have exactly $k$ edges and contain $e$ .

Solution

None

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.