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16 - Sunflowers

from Part II - Extremal Set Theory and Hypergraph Theory

Published online by Cambridge University Press:  10 July 2026

Dhruv Mubayi
Affiliation:
University of Illinois, Chicago
Jacques A. Verstraete
Affiliation:
University of California, San Diego
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Summary

An r-sunflower is a collection of sets such that there is a set C (possibly the empty set) called the core, for which every two of the sets have intersection exactly C. Sunflowers are one of the most important structures in extremal set theory since they are the only configuration that one is guaranteed to contain in any sufficiently large collection of k-elements sets. The simple structure of a sunflower enables one to prove many theorems in combinatorics and beyond. This chapter considers the basic theory of sunflowers, culminating in recent breakthroughs.

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  • Sunflowers
  • Dhruv Mubayi, University of Illinois, Chicago, Jacques A. Verstraete, University of California, San Diego
  • Book: Extremal Graph and Hypergraph Theory
  • Online publication: 10 July 2026
  • Chapter DOI: https://doi.org/10.1017/9781009585835.021
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  • Sunflowers
  • Dhruv Mubayi, University of Illinois, Chicago, Jacques A. Verstraete, University of California, San Diego
  • Book: Extremal Graph and Hypergraph Theory
  • Online publication: 10 July 2026
  • Chapter DOI: https://doi.org/10.1017/9781009585835.021
Available formats
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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.

  • Sunflowers
  • Dhruv Mubayi, University of Illinois, Chicago, Jacques A. Verstraete, University of California, San Diego
  • Book: Extremal Graph and Hypergraph Theory
  • Online publication: 10 July 2026
  • Chapter DOI: https://doi.org/10.1017/9781009585835.021
Available formats
×