An expander is a sparse (low degree) graph with high "expansion," measured in one of several ways; typically akin to the minimum ratio of the size of a subgraph boundary to the subgraph's volume.

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Regularity Lemma for Sparse Graphs

Szemeredi's Regularity Lemma says that every dense graph can be approximated as a union of $O(1)$ many bipartite expander graphs. More accurately, there's a partition of most vertices into $O(1)$ sets ...
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Bi-partite expander graphs

My question relates to bi-partite expander graphs, defined as bi-partite graphs on $n$ left vertices, $m$ right vertices, constant left-degree $k$, such that For any linear-sized subset $S$ of the ...
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expansion with respect to p-norms for p other than 2

Suppose I have an $d$-regular expander graph with $n$ vertices, where the stochastic version of its adjacency matrix $A$ (with entries $1/d$ and zero) has second eigenvalue $\lambda$. Let $x \in ...
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Pseudorandom object yielding shrinkage in $\ell_p$ norm?

Extractors have the following property: For a random variable $X$ of min-entropy $k$ and a seed $Y$, denote the output of an $(k,\epsilon)$-extractor by $\mathrm{Ext}(X,Y)$. Then ...
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Lossless, constant-degree expanders that expand large sets

It is known how to construct "lossless" unbalanced bipartite expanders with the following properties: the bipartite graph has $n$ left vertices, $m$ right vertices, left-degree $D$, and for all ...
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Minimum weight expander

Expander constructions given an expander which is a sub-graph of a complete graph. Sometimes we don't want to construct an arbitrary expander, want to find an expander inside another given graph. In a ...
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Explicit combinatorial construction minimizing intersection of sets

I'd like to know if anything is known about the following problem: Suppose we choose positive integer $t$ to be constant. Let $S = \{1,2,\dots,n\}$, where $n$ is sufficiently large. Consider a ...
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Expansion of constant-size sets

My question refers to the expansion of constant size sets of an expander graph. Suppose we are given an expander graph with Cheeger constant $\alpha$. What can be said about the edge expansion of sets ...
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Delocalization of eigenvectors in Expanding Graphs

Given an adjacency matrix A, can we say something about whether the eigenvectors corresponding to its highest(or second-highest) eigenvalues are delocalized ? By delocalization I mean that every ...
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