Finding large expanders in graphs: from topological minors to induced subgraphs
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2020
- DOI:
- 10.48550/arXiv.2012.15722
- arXiv:
- arXiv:2012.15722
- Bibcode:
- 2020arXiv201215722L
- Keywords:
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- Mathematics - Combinatorics;
- 05C48;
- 05C83
- E-Print:
- 16 pages, 8 figures