Book contents
- Frontmatter
- Contents
- Preface
- Part I Extremal Graph Theory
- Part II Extremal Set Theory and Hypergraph Theory
- Introduction to Part II
- 11 Posets
- 12 Intersecting Families
- 13 Shadows and Matchings
- 14 Linear Algebra Method
- 15 Algebraic Methods
- 16 Sunflowers
- 17 The Turán Problem for Hypergraphs
- 18 Matchings in Linear Hypergraphs
- 19 Independent Sets in Hypergraphs
- 20 Hypergraph Regularity
- 21 Hypergraph Containers
- 22 Hypergraph Ramsey Theory
- Glossary of Notation
- References
- Index
13 - Shadows and Matchings
from Part II - Extremal Set Theory and Hypergraph Theory
Published online by Cambridge University Press: 10 July 2026
Book contents
- Frontmatter
- Contents
- Preface
- Part I Extremal Graph Theory
- Part II Extremal Set Theory and Hypergraph Theory
- Introduction to Part II
- 11 Posets
- 12 Intersecting Families
- 13 Shadows and Matchings
- 14 Linear Algebra Method
- 15 Algebraic Methods
- 16 Sunflowers
- 17 The Turán Problem for Hypergraphs
- 18 Matchings in Linear Hypergraphs
- 19 Independent Sets in Hypergraphs
- 20 Hypergraph Regularity
- 21 Hypergraph Containers
- 22 Hypergraph Ramsey Theory
- Glossary of Notation
- References
- Index
Summary
A central notion in extremal set theory is the shadow of a family H of k-element subsets of an n-element set. It consists of all the k − 1-element subsets that are contained in some set of H. A matching of H is a collection of pairwise disjoint sets in H, and the matching number of H is the largest size of a matching in H. In this chapter, we discuss the basic problems surrounding shadows and matchings in hypergraphs.
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- Extremal Graph and Hypergraph TheoryWith Ramsey Theory, pp. 229 - 242Publisher: Cambridge University PressPrint publication year: 2026
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