Expanders - how to find them, and what to find in them

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

A graph $G=(V, E)$ is called an expander if every vertex subset U of size up to $|V|/2$ has an external neighborhood whose size is comparable to $|U|$. Expanders have been a subject of intensive research for more than three decades and have become one of the central notions of modern graph theory. We first discuss the above definition of an expander and its alternatives. Then we present examples of families of expanding graphs and state basic properties of expanders. Next, we introduce a way to argue that a given graph contains a large expanding subgraph. Finally we research properties of expanding graphs, such as existence of small separators, of cycles (including cycle lengths), and embedding of large minors.

Original languageEnglish
Title of host publicationSurveys in Combinatorics 2019
EditorsAllan Lo, Richard Mycroft, Guillem Perarnau, Andrew Treglown
PublisherCambridge University Press
Pages115-142
Number of pages28
ISBN (Electronic)9781108649094
ISBN (Print)9781108740722
DOIs
StatePublished - 1 Jan 2019

Publication series

NameLondon Mathematical Society Lecture Note Series
PublisherCambridge University Press
Volume456

Keywords

  • Cycles
  • Expanding graphs
  • Graph minors
  • Paths

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