On torsion in eulerian magnitude homology of Erdos-Renyi random graphs

TL;DR

This paper studies when the eulerian magnitude homology groups of Erdos-Renyi random graphs are torsion-free, introducing a new complex and establishing a vanishing threshold for its shelling.

Contribution

It introduces the eulerian Asao-Izumihara complex and determines the regimes where the homology groups are torsion free in random graphs.

Findings

Established a vanishing threshold for the shelling of the complex

Identified regimes with torsion-free eulerian magnitude homology

Connected complex shelling properties to homology torsion

Abstract

In this paper we investigate the regimes where an Erdos-Renyi random graph has torsion free eulerian magnitude homology groups. To this end, we start be introducing the eulerian Asao-Izumihara complex - a quotient CW-complex whose homology groups are isomorphic to direct summands of the graph eulerian magnitude homology group. We then proceed by producing a vanishing threshold for a shelling of eulerian Asao-Izumihara complex. This will lead to a result establishing the regimes where eulerian magnitude homology of Erdos-Renyi random graphs is torsion free.