Geodesic
Weak embeddings of posets to the Boolean lattice
Discrete mathematics & theoretical computer science, Tome 20 (2018) no. 1

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The goal of this paper is to prove that several variants of deciding whether a poset can be (weakly) embedded into a small Boolean lattice, or to a few consecutive levels of a Boolean lattice, are NP-complete, answering a question of Griggs and of Patkos. As an equivalent reformulation of one of these problems, we also derive that it is NP-complete to decide whether a given graph can be embedded to the two middle levels of some hypercube. 
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     author = {P\'alv\"olgyi, D\"om\"ot\"or},
     title = {Weak embeddings of posets to the {Boolean} lattice},
     journal = {Discrete mathematics & theoretical computer science},
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}
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Pálvölgyi, Dömötör. Weak embeddings of posets to the Boolean lattice. Discrete mathematics & theoretical computer science, Tome 20 (2018) no. 1. doi: 10.23638/DMTCS-20-1-7

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