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A generalization of a Ramsey-type theorem on hypermatchings

✍ Scribed by Paul Baginski

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
93 KB
Volume
50
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

For an r‐uniform hypergraph G define N(G, l; 2) (N(G, l; ℤ~n~)) as the smallest integer for which there exists an r‐uniform hypergraph H on N(G, l; 2) (N(G,l; ℤ~n~)) vertices with clique(H) < l such that every 2‐coloring (ℤ~n~‐coloring) of the edges of H implies a monochromatic (zero‐sum) copy of G. Our results strengthen a Ramsey‐type theorem of Bialostocki and Dierker on zero‐sum hypermatchings. As a consequence, we show that for any n ≥ 2, r ≥ 2, and l > r + 1, N(__n__𝒦, l;2) = N(__n__𝒦, l;ℤ~n~) = (r + 1)n − 1. © 2005 Wiley Periodicals, Inc. J Graph Theory

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