Graph-theoretic perspective on a special class of Steiner Systems

TL;DR

This paper explores a special class of Steiner systems using graph theory, providing explicit constructions and analyzing their 2-coloring properties through hypergraph representations.

Contribution

It introduces new explicit constructions of $S(t-1,t,2t)$ Steiner systems via hypergraph models and studies their coloring characteristics.

Findings

Constructed explicit Steiner systems using hypergraph models

Analyzed 2-coloring properties of the hypergraphs

Provided insights into the combinatorial structure of these systems

Abstract

We study $S(t-1,t,2t)$, which is a special class of Steiner systems. Explicit constructions for designing such systems are developed under a graph-theoretic platform where Steiner systems are represented in the form of uniform hypergraphs. The constructions devised are then used to study the $2$-coloring properties of these uniform hypergraphs.