We present a 'Regular Slice Lemma' which, given a k-graph G , returns a regular ( k − 1 ) -complex J with respect to which G has useful regularity ...

We argue that in many cases much of this complexity can be avoided by using a structure which we call a regular slice instead of the more complicated structure ...

Nov 18, 2014 · We study properties of random subcomplexes of partitions returned by (a suitable form of) the Strong Hypergraph Regularity Lemma, which we call regular slices.

Dec 9, 2015 · We present a 'Regular Slice Lemma' which, given a k -graph GG, returns a regular (k−1)(k−1)-complex JJ with respect to which GG has useful ...

We present a 'Regular Slice Lemma' which, given a k-graph G, returns a regular (k−1)-complex J with respect to which G has useful regularity properties.

Sep 11, 2023 · Given E ⊆ V2 and x ∈ V, let Ex = {y ∈ V : (x,y) ∈ E} be the x-fiber of E. ▷ A graph E ⊆ V2 has VC-dimension ≥ d if there are some.

The advantage of this random subcomplex, which we call a regular slice, is that it does correspond to a vertex partition and a weighted reduced hypergraph. The ...

The objective of this paper is to extend the techniques developed by Nagle, Skokan, and authors and obtain a stronger and more “user friendly” regularity lemma ...

Dec 5, 2024 · ... The Regular Slice Lemma of [3] ensures that every sufficiently large k-graph has a representative regular slice. Given the existence of a ...

Semantic Scholar extracted view of "Tight cycles and regular slices in dense hypergraphs" by Peter Allen et al.