Corpus ID: 59316588

Large Minors in Expanders

@article{Chuzhoy2019LargeMI,
  title={Large Minors in Expanders},
  author={Julia Chuzhoy and Rachit Nimavat},
  journal={ArXiv},
  year={2019},
  volume={abs/1901.09349}
}
In this paper we study expander graphs and their minors. Specifically, we attempt to answer the following question: what is the largest function $f(n,\alpha,d)$, such that every $n$-vertex $\alpha$-expander with maximum vertex degree at most $d$ contains {\bf every} graph $H$ with at most $f(n,\alpha,d)$ edges and vertices as a minor? Our main result is that there is some universal constant $c$, such that $f(n,\alpha,d)\geq \frac{n}{c\log n}\cdot \left(\frac{\alpha}{d}\right )^c$. This bound… Expand

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