Maximum degree and fractional matchings in uniform hypergraphs

Research output: Contribution to journalArticle

85 Citations (Scopus)

Abstract

Let ℋ be a family of r-subsets of a finite set X. Set D(ℋ)= {Mathematical expression}|{E:x∈E∈ℋ}|, (maximum degree). We say that ℋ is intersecting if for any H, H′ ∈ ℋ we have H ∩H′ ≠ 0. In this case, obviously, D(ℋ)≧|ℋ|/r. According to a well-known conjecture D(ℋ)≧|ℋ|/(r-1+1/r). We prove a slightly stronger result. Let ℋ be an r-uniform, intersecting hypergraph. Then either it is a projective plane of order r-1, consequently D(ℋ)=|ℋ|/(r-1+1/r), or D(ℋ)≧|ℋ|/(r-1). This is a corollary to a more general theorem on not necessarily intersecting hypergraphs.

Original languageEnglish
Pages (from-to)155-162
Number of pages8
JournalCombinatorica
Volume1
Issue number2
DOIs
Publication statusPublished - Jun 1981

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Uniform Hypergraph
Hypergraph
Maximum Degree
Fractional
Projective plane
Finite Set
Corollary
Subset
Theorem
Family

Keywords

  • AMS subject classification (1980): 05C65, 05C35, 05B25

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Mathematics(all)
  • Computational Mathematics

Cite this

Maximum degree and fractional matchings in uniform hypergraphs. / Füredi, Z.

In: Combinatorica, Vol. 1, No. 2, 06.1981, p. 155-162.

Research output: Contribution to journalArticle

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