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arXiv · 1110.0224

On a covering problem in the hypercube

Brendon Stanton·Lale Özkahya
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Abstract

In this paper, we address a particular variation of the Turán problem for the hypercube. Alon, Krech and Szabó (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.

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Brendon Stanton, Lale Özkahya. 2011-10-02. On a covering problem in the hypercube. https://arxiv.org/abs/1110.0224

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