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arXiv · 2511.13528

Rankwidth of Graphs with Balanced Separations: Expansion for Dense Graphs

Emile Anand
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Abstract

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.

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Emile Anand. 2025-11-17. Rankwidth of Graphs with Balanced Separations: Expansion for Dense Graphs. https://arxiv.org/abs/2511.13528

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