The Lovász local lemma is a well-known probabilistic technique commonly used to prove
the existence of rare combinatorial objects. We explore the lopsided (or negative …

Abstract The Lovász Local Lemma is known to have an extension for cases where
independence is missing but negative dependencies are under control. We show that this is …

The Lovász local lemma is a powerful and well-studied probabilistic technique useful in
establishing the possibility of simultaneously avoiding every event in some collection. A …

Our previous paper applied a lopsided version of the Lov\'asz Local Lemma that allows
negative dependency graphs to the space of random injections from an $ m $-element set to …

Shearer gave a general theorem characterizing the family article mathrsfs, amsmath,
amssymb empty L of dependency graphs labeled with probabilities pv which have the …

Abstract The Lovász Local Lemma is a very powerful tool in probabilistic combinatorics, that
is often used to prove existence of combinatorial objects satisfying certain constraints. Moser …

An old result by Shearer relates the Lovász local lemma with the independent set
polynomial on graphs, and consequently, as observed by Scott and Sokal, with the partition …

We show that for any graph G, by considering “activation” through the strong product with
another graph H, the relation α (G)≤ ϑ (G) between the independence number and the …

In this paper we investigate the extent to which the Lovász Local Lemma (an important tool
in probabilistic combinatorics) can be adapted for the measurable setting. In most …

Let $ H_d (n, p) $ signify a random $ d $-uniform hypergraph with $ n $ vertices in which
each of the ${n}\choose {d} $ possible edges is present with probability $ p= p (n) …