Ramsey-Style Hypergraph Partition Bound H(n)

Let $H(n)$ be the largest number of vertices in a hypergraph with no isolated vertices and no partition of size greater than $n$. With $k_1 = 1$ and $k_n = \lfloor n/2 \rfloor + k_{\lfloor n/2 \rfloor} + k_{\lceil n/2 \rceil}$, prove $H(n) \ge c\,k_n$ for some constant $c > 1$, already for $n = 15$, with a constructive algorithm.

Result

Proved

Status

Resolved

AI contribution

AI-discovered

Method

Construction

Field

Extremal combinatorics

Posed by

—

Year posed

2019

Years open

7y

Solved

2026-03-24

Model

GPT-5.4 Pro

Vendor

OpenAI

Collaborators

—

Verification

Unreviewed

Publication

Announced

Significance

10 / 100*

Disclosed cost

—

Wikipedia

No dedicated article