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We show that every edge in a 4‐connected planar graph on vertices is contained in at least cycles of pairwise distinct lengths. We also show that this number can be at best. In the case of 4‐connected planar graphs not containing a 4‐cycle, we show that any such graph on vertices contains at least cycles of pairwise distinct lengths.
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Mohar et al. (2026) studied this question.
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