Show by counterexample that filtering based on given theorem

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Show by counterexample that filtering based on Theorem 3.41 is incomplete, even when all separators are used.

Theorem 3.41
If S is a separator of directed graph G, then G contains a hamiltonian cycle only if GS contains a permissible hamiltonian cycle.

Furthermore, an edge of G connecting vertices in S is hamiltonian only if it is part of a permissible hamiltonian cycle of GS.

Reference no: EM131168837

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