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# Number of Hamiltonian paths

Let $G$ be an undirected graph on at least five vertices let and $\overline{G}$ its complement. Let $h(G)$ be the number of Hamiltonian paths of $G$.

• Prove that $h(G) + h(\overline{G})$ is even.
Level:
Source: from book "Combinatorial Problems and Exercises"
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Shiva Kintali
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Posted: Aug 01 '12

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Last updated: Aug 01 '12