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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.15213 |
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| _version_ | 1866912240048799744 |
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| author | Pokharanakar, Mugdha Mahesh |
| author_facet | Pokharanakar, Mugdha Mahesh |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15213 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The dual Cheeger-Buser inequality for graphons Pokharanakar, Mugdha Mahesh Combinatorics 05C50 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. |
| title | The dual Cheeger-Buser inequality for graphons |
| topic | Combinatorics 05C50 |
| url | https://arxiv.org/abs/2502.15213 |