The sensitivity of a Boolean function f is the maximum over all inputs x, of the number of
sensitive coordinates of x. The well-known sensitivity conjecture of Nisan (see also Nisan …

We consider the problem of finding a homomorphism from an input digraph G to a fixed
digraph H. We show that if H admits a weak-near-unanimity polymorphism φ then deciding …

Given two non-empty graphs $ H $ and $ T $, write $ H\succcurlyeq T $ to mean that $ t (H,
G)^{| E (T)|}\geq t (T, G)^{| E (H)|} $ for every graph $ G $, where $ t (\cdot,\cdot) $ is the …

The book reviews inequalities for weighted entry sums of matrix powers. Applications range
from mathematics and CS to pure sciences. It unifies and generalizes several results for …

Hoffman [7] proved a matrix inequality that yields a useful upper bound on the number of
walks in a graph. Sidorenko [14] extended the bound on the number of walks to a bound on …

We use an inequality of Sidorenko to show a general relation between local and global
subgraph counts and degree moments for locally weakly convergent sequences of sparse …

Let $\hom (H, G) $ denote the number of homomorphisms from a graph $ H $ to a graph $ G
$. Sidorenko's conjecture asserts that for any bipartite graph $ H $, and a graph $ G $ we …

In the study of graph indexed random walks, two conjectures on the average range of some
functions on graphs and bipartite graphs are posed by Loebl-Nešetril-Reed and by …

We use an inequality of Sidorenko to show a general relation between local and global
subgraph counts and degree moments for locally weakly convergent sequences of sparse …

For graphs G and H, an H-coloring of G is an adjacency preserving map from the vertices of
G to the vertices of H. H-colorings generalize such notions as independent sets and proper …