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

Abstract

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 $cl(G)$.