Closure concept for 2-factors in claw-free graphs

We introduce a closure concept for 2-factors in claw-free graphs that generalizes the closure introduced by the first author. The 2-factor closure of a graph is uniquely determined and the closure operation turns a claw-free graph into the line graph of a graph containing no cycles of length at most 5 and no cycles of length 6 satisfying a certain condition. A graph has a 2-factor if and only if its closure has a 2-factor; however, the closure operation preserves neither the minimum number of components of a 2-factor nor the hamiltonicity or nonhamiltonicity of a graph.