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math.PR2018
A counterexample to the DeMarco-Kahn Upper Tail Conjecture
Matas Šileikis, Lutz Warnke
Given a fixed graph H, what is the (exponentially small) probability that the number X_H of copies of H in the binomial random graph G_{n,p} is at least twice its mean? Studied int…
math.CO2018
Large girth approximate Steiner triple systems
Tom Bohman, Lutz Warnke
In 1973 Erdos asked whether there are n-vertex partial Steiner triple systems with arbitrary high girth and quadratically many triples. (Here girth is defined as the smallest integ…