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The study of probability distributions over graphs. For example, the Erdős–Rényi model where each edge occurs independently with equal probability.

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Does "epsilon-regular" equal to "cut distance less than epsilon"?

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|\ …
tom jerry's user avatar
  • 349
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Another version of Sidorenko's conjecture(?)

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 prop …
tom jerry's user avatar
  • 349
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Does Forcing conjecture equals to assume the host graph is regular?

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, …
tom jerry's user avatar
  • 349