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Paper detail

On a covering problem in the hypercube

In this paper, we address a particular variation of the Turán problem for the hypercube. Alon, Krech and Szabó (2007) asked &#34;In an n-dimensional hypercube, Qn, and for l < d < n, what is the size of a smallest set, S, of Q_l&#39;s so that every Q_d contains at least one member of S?&#34; Likewise, they asked a similar Ramsey type question: &#34;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?&#34; We give upper and lower bounds for each of these questions and provide constructions of the set S above for some specific cases.

preprint2011arXivOpen access
Brendon StantonLale Özkahya
math.CO
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Brendon StantonLale Özkahya

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