Largest density of a layered subgraph of a hypercube

Maria Axenovich; Arsenii Sagdeev

Largest density of a layered subgraph of a hypercube

Combinatorics 2026-07-17 v1

Authors: Maria Axenovich , Arsenii Sagdeev

Abstract

Let $L(t)$ denote the largest number of edges induced by $t$ vertices from two vertex layers of a hypercube. We show that $\frac14 t\log_2 t+\frac18 t\log_2\log_2 t-O(t) \leq L(t) \leq \frac14 t\log_2 t+ (1+o(1))t\log_2\log_2 t.$

Keywords

hypercube layered subgraph induced edges extremal combinatorics density

Cite

@article{arxiv.2607.16556,
  title  = {Largest density of a layered subgraph of a hypercube},
  author = {Maria Axenovich and Arsenii Sagdeev},
  journal= {arXiv preprint arXiv:2607.16556},
  year   = {2026}
}

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5 pages