A note on $m$-factorizations of complete multigraphs arising from designs

TL;DR

This paper introduces new infinite families of indecomposable m-factorizations of complete multigraphs, primarily derived from finite geometries, expanding the understanding of graph decompositions.

Contribution

It presents novel infinite families of indecomposable m-factorizations of complete multigraphs using finite geometry methods.

Findings

New infinite families of indecomposable m-factorizations

Most constructions originate from finite geometries

Advances understanding of graph decompositions

Abstract

Some new infinite families of simple, indecomposable $m$-factorizations of the complete multigraph $\lambda K_v$ are presented. Most of the constructions come from finite geometries.