Geodesic
DP-colorings of uniform hypergraphs and splittings of Boolean hypercube into faces
Vladimir N. Potapov1
1Sobolev Institute of Mathematics
The electronic journal of combinatorics, Tome 29 (2022) no. 3
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We develop a connection between DP-colorings of $k$-uniform hypergraphs of order $n$ and coverings of $n$-dimensional Boolean hypercube by pairs of antipodal $(n-k)$-dimensional faces. Bernshteyn and Kostochka established a lower bound on the number of edges in a non-2-DP-colorable $k$-uniform hypergraph namely, $2^{k-1}$ for odd $k$ and $2^{k-1}+1$ for even $k.$ They proved that these bounds are tight for $k=3,4$. In this paper, we prove that the bound is achieved for all odd $k\geq 3$.
DOI : 10.37236/10550
Classification : 05C15
Mots-clés : DP-coloring, hypergraph, hypercube

Vladimir N. Potapov  1

1 Sobolev Institute of Mathematics 
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Vladimir N. Potapov. DP-colorings of uniform hypergraphs and splittings of Boolean hypercube into faces. The electronic journal of combinatorics, Tome 29 (2022) no. 3. doi: 10.37236/10550

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