Finding large expanders in graphs: from topological minors to induced subgraphs
Combinatorics
2023-02-22 v1
Abstract
In this paper, we consider a structural and geometric property of graphs, namely the presence of large expanders. The problem of finding such structures was first considered by Krivelevich [SIAM J. Disc. Math. 32 1 (2018)]. Here, we show that the problem of finding a large induced subgraph that is an expander can be reduced to the simpler problem of finding a topological minor that is an expander. Our proof is constructive, which is helpful in an algorithmic setting. We also show that every large subgraph of an expander graph contains a large subgraph which is itself an expander.
Cite
@article{arxiv.2012.15722,
title = {Finding large expanders in graphs: from topological minors to induced subgraphs},
author = {Baptiste Louf and Fiona Skerman},
journal= {arXiv preprint arXiv:2012.15722},
year = {2023}
}
Comments
16 pages, 8 figures