Construction of a Non-2-colorable k-uniform Hypergraph with Few Edges

TL;DR

This paper presents a method to construct large non-2-colorable k-uniform hypergraphs with relatively few edges, which also translates into creating unsatisfiable monotone k-CNF formulas with fewer clauses.

Contribution

It introduces a novel construction of non-2-colorable hypergraphs with exponentially fewer edges than previously known, linking hypergraph properties to satisfiability of monotone formulas.

Findings

Constructed non-2-colorable hypergraphs with (2^(1 + o(1)))^k edges

Established a duality between hypergraphs and monotone k-CNF formulas

Produced unsatisfiable monotone k-CNF formulas with fewer clauses

Abstract

We show how to construct a non-2-colorable k-uniform hypergraph with (2^(1 + o(1)))^k edges. By the duality of hypergraphs and monotone k-CNF-formulas this gives an unsatisfiable monotone k-CNF with (2^(1 + o(1)))^k clauses