Edge colorings of r -uniform hypergraphs naturally de¯ne a multicolor-ing on the 2-shadow, i.e. on the pairs that are covered by hyperedges. We
show that in any (r¡1)-coloring of the edges of an r
-uniform hypergraph with n vertices and at least (1¡²)
¡nr¢ edges, the 2-shadow has a monochro-matic matching covering all but at most o(n) vertices. This result implies
that for any fixed r and suffciently large n, there is a monochromatic Berge-cycle of length (1¡ o(1))n in every (r ¡ 1)-coloring of the edges of
, the complete r-uniform hypergraph on n
, Sárközy, Gábor N.
, Szemerédi, Endre
(2007). Monochromatic matchings in the shadow graph of almost complete hypergraphs. .
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