Iterated line graphs are maximally ordered

A graph G is k‐ordered if for every ordered sequence of k vertices, there is a cycle in G that encounters the vertices of the sequence in the given order. We prove that if G is a connected graph distinct from a path, then there is a number t_G such that for every t ≥ t_G the t‐iterated line graph of G, L^t (G), is (δ(L^t (G)) + 1)‐ordered. Since there is no graph H which is (δ(H)+2)‐ordered, the result is best possible. © 2006 Wiley Periodicals, Inc. J Graph Theory 52: 171–180, 2006