  An L-factor of a graph G is a spanning subgraph of G whose every component is
a 3-vertex path. Let v(G) denote the number of vertices of G. A graph is called
claw-free if it does not have a subgraph isomorphic to the graph with 4
vertices and 3 edges having a common vertex. Our results include the following.
Let G$ be a 3-connected claw-free graph, x be a vertex, e = xy be an edge, and
P be a 3-vertex path in G. Then (c1) if v(G) = 0 mod 3, then G has an L-factor
containing (avoiding) e, (c2) if v(G) = 1 mod 3, then G - x has a L-factor,
(c3) if v(G) = 2 mod 3, then G - x -y has an L-factor, (c4) if v(G) = 0 mod 3
and G is either cubic or 4-connected, then G - P has an L-factor, and (c5) if G
is cubic and E is a set of three edges in G, then G - E has an L -factor if and
only if the subgraph induced by E in G is not a claw and not a triangle.
  Keywords: claw-free graph, cubic graph, L-packing, L-factor.
