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

Giuliamaria Menara

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arXiv · 2409.03472

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

Giuliamaria Menara

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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.

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Giuliamaria Menara. 2024-09-05. On torsion in eulerian magnitude homology of Erdos-Renyi random graphs. https://arxiv.org/abs/2409.03472

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