On components of 2-factors in claw-free graphs

For a non-hamiltonian claw-free graph G with order n and minimum degree δ we show the following. If δ=4, then G has a 2-factor with at most (5n−14)/18 components, unless G belongs to a finite class of exceptional graphs. If δ⩾5, then G has a 2-factor with at most (n−3)/(δ−1) components. These bounds are sharp in the sense that we can replace nor 5/18 by a smaller quotient nor δ−1 by δ.