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### Proofs of parity results via the Handshaking lemma

I particularly like the following strategy to prove that the number of some combinatorial objects is even: to construct a graph, in which they correspond to vertices of odd degree (=valency).
Let me ...

**6**

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**2**answers

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### How hard is it to solve SAT if the promise is that it has an odd number of solutions?

SAT is NP-complete even if we promise that it has an even number of solutions (by introducing a new dummy variable). However, USAT (when the promise is that it has exactly one solution) is not known ...