For each k >= 4, every 1-tough (k-1)-connected (P2 cup kP1)-free graph on at least k^2 + k + 1 vertices with minimum degree k is Hamiltonian.
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On hamiltonian cycles of 1-tough $(P_{2} \cup kP_{1})$-free graphs
For each k >= 4, every 1-tough (k-1)-connected (P2 cup kP1)-free graph on at least k^2 + k + 1 vertices with minimum degree k is Hamiltonian.