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edit approved Jan 9, 2016 at 18:02

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No, consider the Petersen graphPetersen graph and another with no star in the middle but just a simple pentagon. The former has no 4-cycle, but the latter has one.

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created Jan 9, 2016 at 17:21

JWL

No, consider the Petersen graph and another with no star in the middle but just a simple pentagon. The former has no 4-cycle, but the latter has one.