# Article

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Keywords:
matching; factors; Hamiltonian cycles; powers of graphs; connected graph
Summary:
The following result is proved: Let \$G\$ be a connected graph of order \$geq 4\$. Then for every matching \$M\$ in \$G^4\$ there exists a hamiltonian cycle \$C\$ of \$G^4\$ such that \$E(C)\bigcap M=0\$.
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