22 citations · 22 across the 1 of their papers we have counts for
5 papers
Note on Sunflowers
Tolson Bell, Suchakree Chueluecha, Lutz Warnke
A sunflower with p petals consists of p sets whose pairwise intersections are identical. The goal of the sunflower problem is to find the smallest r=r(p,k) such that any family of…
On Wormald's differential equation method
Lutz Warnke
This note contains a short and simple proof of Wormald's differential equation method (that yields slightly improved approximation guarantees and error probabilities). This powerfu…
Upper tail bounds for Stars
Matas Šileikis, Lutz Warnke
For r \ge 2, let X be the number of r-armed stars K_{1,r} in the binomial random graph G_{n,p}. We study the upper tail \Pr(X \ge (1+ε)\E X), and establish exponential bounds which…
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…
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…