H-Decompositions

TL;DR

This paper proves that for any graph H with n vertices, the complete graph with 2n+1 vertices can be decomposed into copies of H, establishing a universal decomposition result.

Contribution

It introduces a universal decomposition theorem for complete graphs of size 2n+1 into any graph H of size n, expanding understanding of graph decompositions.

Findings

Complete graph $K_{2n+1}$ can be decomposed into any graph H of size n.

The decomposition exists for all graphs H of size n.

Provides a constructive proof for the decomposition.

Abstract

We show that for all graphs H of size n, the complete graph $K_{2n+1}$ has an $H$-decomposition.