## Abstract

A theorem of Lovász asserts that τ(H)/τ* (H)≤r/2 for every r-partite hypergraph H (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 (V_{1},...,V_{k}) of the vertex set and a partition p_{1} +...+ p_{k} of r such that |e∩V_{i}|≤p_{i}≤r/2 for every edge e and every 1≤i≤k. Moreover, strict inequality holds when r>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 for k-colourable, strongly k-colourable and (what we call) k-partitionable hypergraphs.

Original language | English |
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Pages (from-to) | 149-174 |

Number of pages | 26 |

Journal | Combinatorica |

Volume | 16 |

Issue number | 2 |

DOIs | |

State | Published - 1996 |