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For an integer k with k≥2 and a pair of connected graphs F1 and F2 of order at least three, we say that {F1,F2} is a k-forbidden pair if every k-connected {F1,F2}-free graph, except possibly for a finite number of exceptions, is Hamiltonian. If no exception arises, {F1,F2} is said to be a strong k-forbidden pair. The 2-forbidden pairs and the strong 2-forbidden pairs are determined by Faudree and...
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