High Girth Hypergraphs with Unavoidable Monochromatic or Rainbow Edges
نویسنده
چکیده
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 girth at least g such that in any coloring of its vertices there is either a monochromatic or a rainbow (totally multicolored) edge. We give a probabilistic and a deterministic proof of this result.
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تاریخ انتشار 2016