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On s-Hamiltonian Line Graphs



For an integer s ≥ 0, a graph G is s-hamiltonian if for any vertex subset math formula with |S| ≤ s, G - S is hamiltonian. It is well known that if a graph G is s-hamiltonian, then G must be (s+2)-connected. The converse is not true, as there exist arbitrarily highly connected nonhamiltonian graphs. But for line graphs, we prove that when s ≥ 5, a line graph is s-hamiltonian if and only if it is (s+2)-connected.