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We formulate and prove inverse mixing lemmas in the settings of simplicial complexes and k-uniform hypergraphs. In the hypergraph setting, we extend results of Bilu and Linial for graphs. In the simplicial complex setting, our results answer a question of Parzanchevski et al.
We design an algorithm for computing connectivity in hypergraphs which runs in time $hat O_r(p + min{lambda^{frac{r-3}{r-1}} n^2, n^r/lambda^{r/(r-1)}})$ (the $hat O_r(cdot)$ hides the terms subpolynomial in the main parameter and terms that depend o
Let $F$ be a graph. A hypergraph is called Berge $F$ if it can be obtained by replacing each edge in $F$ by a hyperedge containing it. Given a family of graphs $mathcal{F}$, we say that a hypergraph $H$ is Berge $mathcal{F}$-free if for every $F in m
An oriented hypergraph is an oriented incidence structure that extends the concepts of signed graphs, balanced hypergraphs, and balanced matrices. We introduce hypergraphic structures and techniques that generalize the circuit classification of the s
In this paper, we prove that for any $kge 3$, there exist infinitely many minimal asymmetric $k$-uniform hypergraphs. This is in a striking contrast to $k=2$, where it has been proved recently that there are exactly $18$ minimal asymmetric graphs.
We establish a so-called counting lemma that allows embeddings of certain linear uniform hypergraphs into sparse pseudorandom hypergraphs, generalizing a result for graphs [Embedding graphs with bounded degree in sparse pseudorandom graphs, Israel J.