Claims

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2005_03_21_verstraete: Verstraëte proves that some set of integers with O(n^0.99) elements up to n is unavoidable, in that every graph of average degree at least ten has a cycle whose length lies in it, which answers Problem 72 affirmatively.

2020_10_29_liu_montgomery: Liu and Montgomery prove that every increasing sequence of even integers of at most stretched-exponential growth, the powers of two among them, is unavoidable at large average degree: an explicit density-zero set for 72.

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