Recently, it became apparent that a large number of the most interesting structures and
phenomena of the world can be described by networks. To develop a mathematical theory of …

The History of Degenerate (Bipartite) Extremal Graph Problems Page 1 BOLYAI SOCIETY
Erdos Centennial MATHEMATICAL STUDIES, 25 pp. 169–264. The History of Degenerate (Bipartite) …

For any fixed simple graph H=(V, E) and any fixed u> 0, we establish the leading order of the
exponential rate function for the probability that the number of copies of H in the Erdős …

We revisit the fundamental Boolean Matrix Multiplication (BMM) problem. With the invention
of algebraic fast matrix multiplication over 50 years ago, it also became known that BMM can …

A beautiful conjecture of Erdős-Simonovits and Sidorenko states that, if H is a bipartite
graph, then the random graph with edge density p has in expectation asymptotically the …

The following question is due to Chatterjee and Varadhan (2011). Fix and take, the Erdős‐
Rényi random graph with edge density p, conditioned to have at least as many triangles as …

A bipartite graph H is said to have Sidorenko's property if the probability that the uniform
random map** from V (H) to the vertex set of any graph G is a homomorphism is at least …

Given a graph H on vertex set {1, 2,⋯, n} and a function f:[0, 1] 2→ R, define‖ f‖ H:=|∫∏
ij∈ E (H) f (xi, xj) d μ| V (H)|| 1/| E (H)|, where μ is the Lebesgue measure on [0, 1]. We say …

In this paper, we present several density-type theorems which show how to find a copy of a
sparse bipartite graph in a graph of positive density. Our results imply several new bounds …

We investigate the famous conjecture by Erd\H os-Simonovits and Sidorenko using
information theory. Our method gives a unified treatment for all known cases of the …