Semi-Strong Colouring of Intersecting Hypergraphs

Published: 01 Jan 2014, Last Modified: 06 Feb 2025Comb. Probab. Comput. 2014EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: For any c ≥ 2, a c-strong colouring of the hypergraph G is an assignment of colours to the vertices of G such that, for every edge e of G, the vertices of e are coloured by at least min{c,|e|} distinct colours. The hypergraph G is t-intersecting if every two edges of G have at least t vertices in common.A natural variant of a question of Erdős and Lovász is: For fixed c ≥ 2 and t ≥ 1, what is the minimum number of colours that is sufficient to c-strong colour any t-intersecting hypergraphs? The purpose of this note is to describe some open problems related to this question.
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