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Lifting and Folding: A Framework for Unstable Graphs and TF-Cousins
A graph $G$ is unstable if its canonical double cover, CDC$(G)$, has strictly more automorphisms than Aut$(G)\times\mathbb{Z}_2$. A related question is whether two non-isomorphic graphs can share the same CDC. We place both problems in a unified framework of lifting and guided folding, showing that
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