Erdős Problem #72 — A sparse universal set of cycle lengths

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Does there exist a zero-density set AA of positive integers and a constant c(A)c(A) such that every sufficiently large graph with average degree at least 2c(A)2c(A) contains a cycle whose length lies in AA?

References

Additional references

P. Erdős, Some of my favourite problems in number theory, combinatorics, and geometry, Resenhas 2 (1995), 165–186.

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