A note on 2-subset-regular self-complementary 3-uniform hypergraphs

TL;DR

This paper characterizes the existence of 2-subset-regular self-complementary 3-uniform hypergraphs, establishing precise conditions based on the number of vertices and their congruence properties.

Contribution

It provides a complete characterization of when such hypergraphs exist, filling a gap in the combinatorial understanding of these structures.

Findings

Existence if and only if n ≥ 6 and n ≡ 2 (mod 4)

Established necessary and sufficient conditions for these hypergraphs

Clarified the relationship between vertex count and hypergraph properties

Abstract

We show that a 2-subset-regular self-complementary 3-uniform hypergraph with $n$ vertices exists if and only if $n\ge 6$ and $n$ is congruent to 2 modulo 4.