The dual Cheeger-Buser inequality for graphons

We introduce the notion of bipartiteness ratio for graphons. We prove the dual Cheeger-Buser inequality for graphons, which relates the gap between $2$ and the top of the spectrum of the Laplacian of a graphon with its bipartiteness ratio. The dual Cheeger-Buser inequality was established by Trevisan and Bauer-Jost for graphs. Our result is an analog of that for graphons.

Publication Details

Journal
ArXiv.org
Published
2025-02-20
Primary Topic
Graph theory and applications
Type
article
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article

The dual Cheeger-Buser inequality for graphons

ArXiv.org
Graph theory and applications
article

The dual Cheeger-Buser inequality for graphons

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Abstract

We introduce the notion of bipartiteness ratio for graphons. We prove the dual Cheeger-Buser inequality for graphons, which relates the gap between $2$ and the top of the spectrum of the Laplacian of a graphon with its bipartiteness ratio. The dual Cheeger-Buser inequality was established by Trevisan and Bauer-Jost for graphs. Our result is an analog of that for graphons.

ArXiv.org
Reduced inequalities
Openalex Percentile: Top 44%
Graph theory and applications
Open Access PDFOpenAlex
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The dual Cheeger-Buser inequality for graphons · ArXiv.org (2025) | TGRS Research Map | TGRS