Combinatorica

, Volume 16, Issue 2, pp 149–174 | Cite as

On a theorem of lovász on covers inr-partite hypergraphs

  • Ron Aharoni
  • Ron Holzman
  • Michael Krivelevich
Article

Abstract

A theorem of Lovász asserts that τ(H)/τ*(H)≤r/2 for everyr-partite hypergraphH (where τ and τ* denote the covering number and fractional covering number respectively). Here it is shown that the same upper bound is valid for a more general class of hypergraphs: those which admit a partition (V1, ...,V k ) of the vertex set and a partitionp1+...+p k ofr such that |eV i |≤p i r/2 for every edgee and every 1≤ik. Moreover, strict inequality holds whenr>2, and in this form the bound is tight. The investigation of the ratio τ/τ* is extended to some other classes of hypergraphs, defined by conditions of similar flavour. Upper bounds on this ratio are obtained fork-colourable, stronglyk-colourable and (what we call)k-partitionable hypergraphs.

Mathematics Subject Classification (1991)

05 C 65 05 D 15 

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References

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Copyright information

© Akadémiai Kiadó 1996

Authors and Affiliations

  • Ron Aharoni
    • 1
  • Ron Holzman
    • 1
  • Michael Krivelevich
    • 2
  1. 1.Department of MathematicsTechnion-Israel Institute of TechnologyHaifaIsrael
  2. 2.Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael

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