Abstract
We prove that for every graph H with the minimum degree δ ⩾ 5 , the third iterated line graph L 3 ( H ) of H contains K δ ⌊ δ - 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 1 2 δ ( L i ( G ) ) -linked. Since the degree of L i ( G ) is even, the result is best possible.
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