Table of Contents
International Journal of Combinatorics
Volume 2013, Article ID 929565, 6 pages
http://dx.doi.org/10.1155/2013/929565
Research Article

Gallai-Colorings of Triples and 2-Factors of

1Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA
2Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, P.O. Box 127, Budapest 1364, Hungary
3Department of Mathematics, North Carolina State University, P.O. Box 8205, Raleigh, NC 27695, USA

Received 5 June 2013; Accepted 3 August 2013

Academic Editor: R. Yuster

Copyright © 2013 Lynn Chua et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A coloring of the edges of the -uniform complete hypergraph is a -coloring if there is no rainbow simplex; that is, every set of vertices contains two edges of the same color. The notion extends -colorings which are often called Gallai-colorings and originates from a seminal paper of Gallai. One well-known property of -colorings is that at least one color class has a spanning tree. J. Lehel and the senior author observed that this property does not hold for -colorings and proposed to study , the size of the largest monochromatic component which can be found in every -coloring of , the complete -uniform hypergraph. The previous remark says that and in this note, we address the case . We prove that and this determines for . We also prove that by excluding certain 2-factors from the middle layer of the Boolean lattice on seven elements.