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arXiv · 2012.15722

Finding large expanders in graphs: from topological minors to induced subgraphs

Baptiste Louf·Fiona Skerman
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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.

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Baptiste Louf, Fiona Skerman. 2020-12-31. Finding large expanders in graphs: from topological minors to induced subgraphs. https://doi.org/10.37236/10859

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