Document Type

Article

Publication Date

8-2-2007

Abstract

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

K(r)n

, the complete r-uniform hypergraph on n

vertices.

DOI

WPI-CS-TR-07-15

Share

 
COinS