pith. sign in

Triangle-free subsets of the $r$-distance graph of the Hypercube

· 2025 · math.CO · arXiv 2506.18782

1 Pith paper cite this work. Polarity classification is still indexing.

1 Pith paper citing it
open full Pith review browse 1 citing papers arXiv PDF
abstract

Given the $r$-distance graph on the hypercube $\mathbb{F}_2^n$, where two vertices are adjacent if their Hamming distance is exactly $r$, we study the maximum size $T(n,r)$ of a triangle-free set of vertices. For even $r\le n/2$, we prove \[T(n,r)=O\!\left(\frac{r2^n}{n+1}\right).\] We also obtain lower bounds in various regimes of $r$ as a function of $n$.

fields

math.CO 1

years

2026 1

verdicts

UNVERDICTED 1

representative citing papers

Forbidding Exactly One Hamming Distance

math.CO · 2026-04-07 · unverdicted · novelty 6.0

The s-independence number of the exact-r-distance graph on the hypercube is asymptotically Θ(2^n / n^{r/2}) for fixed s ≥ 2 and even r ≥ 2.

citing papers explorer

Showing 1 of 1 citing paper.

  • Forbidding Exactly One Hamming Distance math.CO · 2026-04-07 · unverdicted · none · ref 27 · internal anchor

    The s-independence number of the exact-r-distance graph on the hypercube is asymptotically Θ(2^n / n^{r/2}) for fixed s ≥ 2 and even r ≥ 2.