The threshold for G(n,p) arrow (mH)_2 is n^{-1/max{m2(H),1}} with m approximately n/(2k-alpha), matching the Rodl-Rucinski threshold for most H.
Available as arXiv:2411.14566
2 Pith papers cite this work. Polarity classification is still indexing.
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Determines the threshold for the random subset [n]_p to almost surely inherit the canonical van der Waerden property for k-APs.
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Ramsey properties for tilings in random graphs
The threshold for G(n,p) arrow (mH)_2 is n^{-1/max{m2(H),1}} with m approximately n/(2k-alpha), matching the Rodl-Rucinski threshold for most H.
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A sparse canonical van der Waerden theorem
Determines the threshold for the random subset [n]_p to almost surely inherit the canonical van der Waerden property for k-APs.