Abstract
We study the stability of some classes of graphs defined in terms of forbidden subgraphs under the closure operation introduced by the second author. Using these results, we prove that every 2-connected claw-free and P 7-free, or claw-free and Z 4-free, or claw-free and eiffel-free graph is either hamiltonian or belongs to a certain class of exceptions (all of them having connectivity 2).
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