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Abstract
We study induced non-separating cycles in 2-connected and 3-connected graphs. As consequences, two conjectures of Vince and Little on discrete Jordan curves are solved, in particular, they are true for simple 2-connected graphs with minimum degree at least six (this is best possible). We also disprove a conjecture of Thomassen and Toft about the structure of 2-connected graphs in which all induced cycles are separating.
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