Maybe this is not quite what you want - but Another Hamiltoniain Path says that if there is a Hamiltonian path in G, then there is another one either in G or its complement \bar{G}. The idea is to define an (exponentially large) graph in which Hamiltonian paths correspond to the number of odd-degree vertices. There are an even number of these. So… this is sorta an example of odd parity, but it’s really showing that the set plus one has even parity :-) Cris
On Jan 29, 2020, at 7:44 AM, James Propp <jamespropp@gmail.com> wrote:
What are people’s favorite examples of existence proofs that show that a set is not empty by showing that its cardinality is odd?
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