Hamiltonicity and Minimum Degree in 3-connected Claw-Free Graphs

Using Ryjáčekʹs closure, we prove that any 3-connected claw-free graph of order ν and minimum degree δ⩾ν+3810 is hamiltonian. This improves a theorem of Kuipers and Veldman who got the same result with the stronger hypotheses δ⩾ν+298 and ν sufficiently large and nearly proves their conjecture saying that the result holds as soon as δ⩾ν+610 for ν sufficiently large.