Abstract
We show that every 3-connected claw-free graphs having at most 5δ – 10 vertices is hamiltonian, where δ is the minimum degree. For regular 3-connected claw-free graphs, a related result was obtained by Li and Liu (preprint), but for nonregular claw-free graphs the best-known result comes from the work of Zhang (1988), with n⩽4δ+3.
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