Minor-excluded graphs and soficity

Q: What type of study is this?

This is a Quantitative Study study.

Oriol Solé-Pi

doi:10.48550/arxiv.2508.06731

August 8, 2025Open Access

Minor-excluded graphs and soficity

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Key Points

Every one-ended unimodular random rooted graph that lacks a minor H is proven to be sofic.
The inclusion of quasi-transitive graphs allows dropping the one-ended condition for soficity.
The concept of soficity arises from the Benjamini-Schramm limit of finite graphs.
The study addresses the relationship between minors and the sofic property in random graphs.

Implication

This research shows that unimodular random rooted graphs without a minor, imply soficity, highlighting graph behavior through specific conditions.

Abstract

A random rooted graph is said to be sofic if it is the Benjamini-Schramm limit of a sequence of finite graphs. Given any finite graph H, we prove that every one-ended, unimodular random rooted graph that does not have H as a minor must be sofic. The hypothesis regarding the number of ends can be dropped under the additional assumption that the graph is quasi-transitive.

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Cite This Study

Oriol Solé-Pi (2025) studied this question.

synapsesocial.com/papers/68f12bfb2107091eab27a390 https://doi.org/10.48550/arxiv.2508.06731

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Minor-excluded graphs and soficity

Key Points

Implication

Abstract

Discussion

Cite This Study

Minor-excluded graphs and soficity

Key Points

Implication

Abstract

Discussion

Cite This Study

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