Some results and problems on clique coverings of hypergraphs

TL;DR

This paper investigates the parameter (F), representing the smallest number of cliques needed to cover a hypergraph, providing bounds for different classes of hypergraphs to understand their covering properties.

Contribution

It introduces bounds on (F) for various classes of hypergraphs, advancing understanding of clique coverings in hypergraph theory.

Findings

Derived bounds on (F) for specific hypergraph classes

Identified open problems related to clique coverings of hypergraphs

Extended theoretical understanding of hypergraph covering parameters

Abstract

For a $k$-uniform hypergraph $F$ we consider the parameter $\Theta(F)$, the minimum size of a clique cover of the of $F$. We derive bounds on $\Theta(F)$ for $F$ belonging to various classes of hypergraphs.