On a covering problem in the hypercube
Combinatorics
2011-10-04 v1
Abstract
In this paper, we address a particular variation of the Tur\'an problem for the hypercube. Alon, Krech and Szab\'o (2007) asked "In an n-dimensional hypercube, Qn, and for l < d < n, what is the size of a smallest set, S, of Q_l's so that every Q_d contains at least one member of S?" Likewise, they asked a similar Ramsey type question: "What is the largest number of colors that we can use to color the copies of Q_l in Q_n such that each Q_d contains a Q_l of each color?" We give upper and lower bounds for each of these questions and provide constructions of the set S above for some specific cases.
Cite
@article{arxiv.1110.0224,
title = {On a covering problem in the hypercube},
author = {Brendon Stanton and Lale Özkahya},
journal= {arXiv preprint arXiv:1110.0224},
year = {2011}
}
Comments
8 pages