Linkability in iterated line graphs

We prove that for every graph H with the minimum degree @d>=5, the third iterated line graph L^3(H) of H contains K"@d"@?"@d"-"1"@? as a minor. Using this fact we prove that if G is a connected graph distinct from a path, then there is a number k"G such that for every i>=k"G the i-iterated line graph of G is [email protected](L^i(G))-linked. Since the degree of L^i(G) is even, the result is best possible.