All Questions

Given two graphs $H$ and $G$, the homomorphism density $t(H, G)$ is defined as the proportion of mappings from the vertices of $H$ to the vertices of $G$ that preserve adjacency. Formally, $$ t(H, ...

I would like to ask a question about Sidorenko's conjecture. Here is the background of my question: Quasi-random graphs A sequence of graphs $(G_n)$ is called quasi-random if it satisfies certain ...

Let $G$ be a bipartite graph (vertex number sufficient large) with bipartition $(U,W)$ and edge density $d$. Does these two statement equal? $G$ is $\varepsilon$-regular, i.e. $\big|e_G(X,Y)-d|X||Y|\...

My (philosophical) question arises from reading the wonderful paper of Chung-Graham-Wilson where the authors introduces the notion of quasi-random graphs. The main purpose of the paper is to show ...

(1.) How small can set $S$ of vertices in any regular undirected graph $G$ on $n$ vertices with degree $\Omega(n^\alpha)$ where $\alpha\in(0,1)$ can be such that every edge in the graph is incident on ...