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2 - Basic Tools

from Part I - Preliminaries

Published online by Cambridge University Press:  02 March 2023

Alan Frieze  and
Michał Karoński
Alan Frieze
Affiliation:
Carnegie Mellon University, Pennsylvania
Michał Karoński
Affiliation:
Adam Mickiewicz University, Poznań, Poland
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Summary

Before reading and studying the results on random graphs included in the text one should become familiar with the basic rules of asymptotic computation, find leading terms in combinatorial expressions, choose suitable bounds for the binomials, as well as get acquainted with probabilistic tools needed to study tail bounds, i.e., the probability that a random variable exceeds (or is smaller than) some real value. This chapter offers the reader a short description of these important technical tools used throughout the text.

Keywords

asymptoticscombinatorial expressionsbinomialstail boundsstochastic dominance
Type
Chapter
Information
Random Graphs and Networks: A First Course , pp. 8 - 26
Publisher: Cambridge University Press
Print publication year: 2023

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  • Basic Tools
  • Alan Frieze, Carnegie Mellon University, Pennsylvania, Michał Karoński, Adam Mickiewicz University, Poznań, Poland
  • Book: Random Graphs and Networks: A First Course
  • Online publication: 02 March 2023
  • Chapter DOI: https://doi.org/10.1017/9781009260268.004
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To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • Basic Tools
  • Alan Frieze, Carnegie Mellon University, Pennsylvania, Michał Karoński, Adam Mickiewicz University, Poznań, Poland
  • Book: Random Graphs and Networks: A First Course
  • Online publication: 02 March 2023
  • Chapter DOI: https://doi.org/10.1017/9781009260268.004
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Basic Tools
  • Alan Frieze, Carnegie Mellon University, Pennsylvania, Michał Karoński, Adam Mickiewicz University, Poznań, Poland
  • Book: Random Graphs and Networks: A First Course
  • Online publication: 02 March 2023
  • Chapter DOI: https://doi.org/10.1017/9781009260268.004
Available formats
×