Extensions of Gallai's graph covering theorems for uniform hypergraphs

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Abstract

Let H be an r-uniform hypergraph in which the minimum number of edges covering all vertices is ρ{variant} = ρ{variant}(H). In answering two questions of T. Gallai we prove that 1. (1) every collection M of pairwise disjopint edges (=matching) of H is contained in a covering of size at most (2 - r-1)ρ{variant}, and 2. (2) every maximum matching M of H is contained in a covering of size at most (2 - (r - 1)-1)ρ{variant}. Both estimates are sharp.

Original languageEnglish
Pages (from-to)92-96
Number of pages5
JournalJournal of Combinatorial Theory, Series B
Volume52
Issue number1
DOIs
Publication statusPublished - May 1991

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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