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A known result by the author in 1991 is that every 3-connected claw-free graph on at most 66-11 vertices is Hamiltonian. In this paper it is proved that every 3-connected k-regular claw-free graph on at most 7k -19 vertices is Hamiltonian.doi:10.1016/0012-365x(94)00348-m fatcat:wsxpv4rrxzcbdfedkrwmj5g2pq