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On the Number of Edges in Hypergraphs Critical with Respect to Strong Colourings

✍ Scribed by Alexandr V. Kostochka; Douglas R. Woodall

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 94 KB
Volume: 21
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1999.0330

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✦ Synopsis

A colouring of the vertices of a hypergraph G is called strong if, for every edge A, the colours of all vertices in A are distinct. It corresponds to a colouring of the generated graph (G) obtained from G by replacing every edge by a clique. We estimate the minimum number of edges possible in a k-critical t-uniform hypergraph with a given number of vertices. In particular we show that, for k ≥ t + 2, the problem reduces in a way to the corresponding problem for graphs. In the case when the generated graph of the hypergraph has bounded clique number, we give a lower bound that is valid for sufficiently large k and is asymptotically tight in k; this bound also holds for list strong colourings.

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