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Cheeger constants and bipartiteness ratios of Cayley graphons

  • Mugdha Mahesh Pokharanakar
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Abstract

We show, under a certain assumption, that the Cheeger constant of a connected Cayley graphon is bounded from above in terms of its bipartiteness ratio, and also in terms of the gap between the top of the spectrum of its Laplacian and $2$. Using this result, we prove that if a connected Cayley graphon C(G,γ) is bipartite, then there exists an index two subgroup H of G that avoids the support of γ.

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Cite

BibTeXRIS
BibTeX
@misc{pokharanakar2026cheeger,
  title = {{Cheeger constants and bipartiteness ratios of Cayley graphons}},
  author = {Mugdha Mahesh Pokharanakar},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.01745},
  eprint = {2610.01745},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.01745},
}
RIS
TY  - UNPB
TI  - Cheeger constants and bipartiteness ratios of Cayley graphons
AU  - Mugdha Mahesh Pokharanakar
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.01745
UR  - https://arxiv.org/abs/2610.01745
AB  - We show, under a certain assumption, that the Cheeger constant of a connected Cayley graphon is bounded from above in terms of its bipartiteness ratio, and also in terms of the gap between the top of the spectrum of its Laplacian and $2$. Using this result, we prove that if a connected Cayley graphon C(G,γ) is bipartite, then there exists an index two subgroup H of G that avoids the support of γ.
ER  -