Sidorenko's conjecture states that the number of copies of a bipartite graph H in a graph G is
asymptotically minimised when G is a quasirandom graph. A notorious example where this …

The theory of graphons comes with the so-called cut norm and the derived cut distance. The
cut norm is finer than the weak* topology (when considering the predual of L 1-functions) …

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 …

We say that a graph H dominates another graph H′ if the number of homomorphisms from
H′ to any graph G is dominated, in an appropriate sense, by the number of …

Let ℋ be the class of bounded measurable symmetric functions on 0, 1 2. For a function h∈
ℋ and a graph G with vertex set v 1,⌦, vn and edge set E (G), define t_G (h)= ∫ ⋯ ∫ ∏ {v_i …

A system of linear equations $ L $ is said to be norming if a natural functional $ t_L (\cdot) $
giving a weighted count for the set of solutions to the system can be used to define a norm …

For any given graph HH, one may define a natural corresponding functional∥.∥ H ‖.‖_H
for real‐valued functions by using homomorphism density. One may also extend this to …

Combinatorics is often very broadly defined as the study of finite or discrete structures. While
the earliest combinatorial investigations seem to go back much further [], often Euler's …