A new proof of Delahan's induced-universality result

TL;DR

This paper presents a concise, self-contained proof of Delahan's theorem, demonstrating that every simple graph can be embedded as an induced subgraph within a Steinhaus graph of specific size, using generating index sets.

Contribution

It introduces a new, simplified proof of Delahan's induced-universality theorem based on generating index sets for Steinhaus triangles.

Findings

Every simple graph on n vertices is an induced subgraph of a Steinhaus graph with (n(n-1)/2)+1 vertices.

The proof is shorter and more self-contained than previous proofs.

Uses the concept of generating index sets for Steinhaus triangles.

Abstract

We give a short and self-contained proof of Delahan's theorem stating that every simple graph on $n$ vertices occurs as an induced subgraph of a Steinhaus graph on $\frac{n(n-1)}{2}+1$ vertices. This new proof is obtained by considering the notion of generating index sets for Steinhaus triangles.