High girth hypergraphs with unavoidable monochromatic or rainbow edges
نویسندگان
چکیده
منابع مشابه
High Girth Hypergraphs with Unavoidable Monochromatic or Rainbow Edges
A classical result of Erdős and Hajnal claims that for any integers k, r, g ≥ 2 there is an r-uniform hypergraph of girth at least g with chromatic number at least k. This implies that there are sparse hypergraphs such that in any coloring of their vertices with at most k − 1 colors there is a monochromatic hyperedge. We show that for any integers r, g ≥ 2 there is an r-uniform hypergraph of gi...
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One of the most interesting new developments in hypergraph colourings in these last few years has been Voloshin’s notion of colourings of mixed hypergraphs. In this paper we shall study a specific instance of Voloshin’s idea: a non-monochromatic non-rainbow (NMNR) colouring of a hypergraph is a colouring of its vertices such that every edge has at least two vertices coloured with different colo...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2020
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.2291