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The Uniformity Lemma for hypergraphs

✍ Scribed by P. Frankl; V. Rödl


Publisher
Springer Japan
Year
1992
Tongue
English
Weight
173 KB
Volume
8
Category
Article
ISSN
0911-0119

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Hypergraph colouring and the Lovász Loca
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The Lov~sz Local Lemma yields sufficient conditions for a hypergraph to be 2-colourable, that is, to have a colouring of the points blue or red so that no edge is monochromatic. The method yields a general theorem, which shows for example that, if H is a hypergraph in which each edge contains at lea

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If H is an r-uniform hypergraph of order p without (r + 1)-cliques, then the transversal number of H has an upper bound in terms of the parameter c = p -2r. As corollaries of the main theorem, lower bounds for the largest order of r-uniform hypergraphs with specified transversal number and for the s