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Define two facets of a simplicial sphere as k-connected if there are at least k disjoint edge-vertex paths between them in their facet-ridge graphs.

Do bistellar flips preserve facet k-connectivity?

I believe the answer is required to be "yes" by topological conditions, and I'd be delighted to know that this is an obvious fact for some reason -- or, better still, that I'm mistaken.

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