Closure, Path-Factors and Path Coverings in Claw-Free Graphs

In this paper, we study path-factors and path coverings of a claw-free graph and those of its closure. For a claw-free graph \(G\) and its closure \( cl(G)\), we prove:(1) \(G\) has a path-factor with \(r\) components if and only if \( cl(G)\) has a path-factor with \(r\) components,(2) \(V(G)\) is covered by \(k\) paths in \(G\) if and only if \(V( cl(G))\) is covered by \(k\) paths in \( cl(G)\).