Monochromatic matchings in the shadow graph of almost complete hypergraphs

András Gyárfás, Gábor N. Sárközy, Endre Szemerédi

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Edge colorings of r-uniform hypergraphs naturally define a multicoloring on the 2-shadow, i.e., on the pairs that are covered by hyperedges. We show that in any (r - 1)-coloring of the edges of an r-uniform hypergraph with n vertices and at least edges, the 2-shadow has a monochromatic matching covering all but at most o(n) vertices. This result confirms an earlier conjecture and implies that for any fixed r and sufficiently large n, there is a monochromatic Berge-cycle of length (1 - o(1))n in every (r - 1)-coloring of the edges of Kn(r), the complete r-uniform hypergraph on n vertices.

Original languageEnglish
Pages (from-to)245-249
Number of pages5
JournalAnnals of Combinatorics
Volume14
Issue number2
DOIs
Publication statusPublished - Jun 2010

Keywords

  • Colored complete uniform hypergraphs
  • Monochromatic matchings

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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