Rankwidth of Graphs with Balanced Separations: Expansion for Dense Graphs
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917085709336576 |
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| author | Anand, Emile |
| author_facet | Anand, Emile |
| contents | We prove that every graph of rankwidth at least $72r$ contains an induced subgraph whose minimum balanced cutrank is at least $r$, which implies a vertex subset where every balanced separation has $\mathbb{F}_2$-cutrank at least $r$. This implies a novel relation between rankwidth and a well-linkedness measure, defined entirely by balanced vertex cuts. As a byproduct, our result supports the notion of rank-expansion as a suitable candidate for measuring expansion in dense graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13528 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rankwidth of Graphs with Balanced Separations: Expansion for Dense Graphs Anand, Emile Combinatorics Computational Complexity Discrete Mathematics 05A20 F.1.3; G.2.2 We prove that every graph of rankwidth at least $72r$ contains an induced subgraph whose minimum balanced cutrank is at least $r$, which implies a vertex subset where every balanced separation has $\mathbb{F}_2$-cutrank at least $r$. This implies a novel relation between rankwidth and a well-linkedness measure, defined entirely by balanced vertex cuts. As a byproduct, our result supports the notion of rank-expansion as a suitable candidate for measuring expansion in dense graphs. |
| title | Rankwidth of Graphs with Balanced Separations: Expansion for Dense Graphs |
| topic | Combinatorics Computational Complexity Discrete Mathematics 05A20 F.1.3; G.2.2 |
| url | https://arxiv.org/abs/2511.13528 |