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- W4300996872 abstract "A classical result of ErdH{o}s and Hajnal claims that for any integers $k, r, g geq 2$ 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 $r, ggeq 2$ 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." @default.
- W4300996872 created "2022-10-04" @default.
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- W4300996872 date "2016-07-22" @default.
- W4300996872 modified "2023-09-27" @default.
- W4300996872 title "High girth hypergraphs with unavoidable monochromatic or rainbow edges" @default.
- W4300996872 doi "https://doi.org/10.48550/arxiv.1607.06600" @default.
- W4300996872 hasPublicationYear "2016" @default.
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