#hypergraph theory

4 results
cs.IT2026

Polynomially Improved Lower Bounds for Trifferent Codes via Locally Sparse -Uniform Hypergraphs

Xuejiao Han, Yubo Sun, Gennian Ge

The paper improves the known lower bound on the size of ternary trifferent codes by a factor of √n, using a refined concatenation method that employs locally sparse 3‑uniform hyper…

#trifferent codes#ternary codes#hypergraph theory#lower bounds
math.CO2026

A Spectral Proof of the Hypergraph Moore Bound

Alexander Schmidhuber, Matthew B. Hastings

The paper proves Feige's hypergraph Moore bound conjecture, showing that any sufficiently dense k‑uniform hypergraph contains a small even cover, using new spectral bounds for Kiku…

#hypergraph theory#even cover#Moore bound#spectral methods
math.CO2026

The Hypergraph Moore Bound

Afonso S. Bandeira, Dmitriy Kunisky, Petar Nizić-Nikolac +2

The paper proves Feige’s hypergraph Moore bound for all even uniformities (k ≥ 4) without extra polylogarithmic factors, using colored walks in a Kikuchi graph and a polynomial int…

#hypergraph theory#even cover#Moore bound#graph girth
math.ST2026

Incomplete U-Statistics of Equireplicate Designs: Berry-Esseen Bound and Efficient Construction

Cesare Miglioli, Jordan Awan

The paper develops a hypergraph‑based framework for incomplete U‑statistics, proving a Berry‑Esseen bound that allows Gaussian approximations even in degenerate cases, and provides…

#u-statistics#incomplete u-statistics#hypergraph theory#combinatorial designs