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}
}
• Published 2019
• Mathematics, Computer Science
• ArXiv
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
3 Citations

#### References

SHOWING 1-10 OF 36 REFERENCES
Towards Tight(er) Bounds for the Excluded Grid Theorem
• Mathematics, Computer Science
• SODA
• 2019
A Separator Theorem in Minor-Closed Classes
• Mathematics, Computer Science
• 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
• 2010
Existence and Construction of Edge-Disjoint Paths on Expander Graphs
• Mathematics, Computer Science
• SIAM J. Comput.
• 1994
Edge-disjoint paths in expander graphs
• A. Frieze
• Mathematics, Computer Science
• SODA '00
• 2000
Edge Disjoint Paths in Moderately Connected Graphs
• Mathematics, Computer Science
• SIAM J. Comput.
• 2010
Finding and Using Expanders in Locally Sparse Graphs
Approximation Algorithms for the Edge-Disjoint Paths Problem via Raecke Decompositions
• M. Andrews
• Mathematics, Computer Science
• 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
• 2010