Finding Large Expanders in Graphs: from Topological Minors to Induced Subgraphs

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 a...

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Veröffentlicht in:The Electronic journal of combinatorics 2023, Vol.30 (1)
Hauptverfasser: Louf, Baptiste, Skerman, Fiona
Format: Artikel
Sprache:eng
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Zusammenfassung: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 large 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.
ISSN:1077-8926
1097-1440
1077-8926
DOI:10.37236/10859