Decompositions of 3-uniform hypergraph K_v^{(3)} into hypergraph K_4^{(3)}+e

TL;DR

This paper characterizes the conditions under which a complete 3-uniform hypergraph can be decomposed into a specific smaller hypergraph, providing a complete existence criterion based on the number of vertices.

Contribution

It establishes necessary and sufficient conditions for decomposing K_v^{(3)} into K_4^{(3)}+e hypergraphs, filling a gap in hypergraph decomposition theory.

Findings

Decomposition exists if and only if v ≡ 0, 1, 2 (mod 5) and v ≥ 7.

Provides a complete characterization of such hypergraph decompositions.

Advances understanding of hypergraph decomposition structures.

Abstract

In this paper it is established that a decomposition of a 3-uniform hypergraph K_v^{(3)} into a special kind of hypergraph K_4^{(3)}+e exists if and only if v\equiv 0,1,2 (mod 5) and v\geq 7.