Covering non-uniform hypergraphs

Endre Boros, Yair Caro, Z. Füredi, Raphael Yuster

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

A subset of the vertices in a hypergraph is a cover if it intersects every edge. Let τ(H) denote the cardinality of a minimum cover in the hypergraph H, and let us denote by g(n) the maximum of τ(H) taken over all hypergraphs H with n vertices and with no two hyperedges of the same size. We show thatg(n)k edges with cardinality i for all i=1, 2, ..., n. We prove that g(n, C, k)(k+1)/(k+2).These results have an interesting graph-theoretic application. For a family F of graphs, let T(n, F, r) denote the maximum possible number of edges in a graph with n vertices, which contains each member of F at most r-1 times. T(n, F, 1)=T(n, F) is the classical Turán number. Using the results above, we can compute a non-trivial upper bound for T(n, F, r) for many interesting graph families.

Original languageEnglish
Pages (from-to)270-284
Number of pages15
JournalJournal of Combinatorial Theory. Series B
Volume82
Issue number2
DOIs
Publication statusPublished - Jul 2001

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Hypergraph
Covering
Graph in graph theory
Denote
Cardinality
Cover
Intersect
Upper bound
Subset
Family

Keywords

  • Hypergraph; covering; cycles

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Covering non-uniform hypergraphs. / Boros, Endre; Caro, Yair; Füredi, Z.; Yuster, Raphael.

In: Journal of Combinatorial Theory. Series B, Vol. 82, No. 2, 07.2001, p. 270-284.

Research output: Contribution to journalArticle

Boros, Endre ; Caro, Yair ; Füredi, Z. ; Yuster, Raphael. / Covering non-uniform hypergraphs. In: Journal of Combinatorial Theory. Series B. 2001 ; Vol. 82, No. 2. pp. 270-284.
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