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[PFR19] On the degree sequence of 3-uniform hypergraph

Conférence Internationale avec comité de lecture : 21 st International Conference on Discrete Geometry for Computer Imagery, February 2019, pp.to appear, Series LNCS, France,

Mots clés: h-uniform hypergraph, hypergraph degree sequence, discrete tomography, reconstruction problem

Résumé: The study of the degree sequences of h-uniform hypergraphs, say h-sequences, was a longstanding open problem in the case of h > 2, until very recently where its decision version was proved to be NP- complete. Formally, the decision version of this problem is: Given π = (d1,d2,...,dn) a non increasing sequence of positive integers, is π the degree sequence of a h-uniform simple hypergraph? Now, assuming P ̸= N P , we know that such an effective characterization cannot exist even for the case of 3-uniform hypergraphs. However, several necessary or sufficient conditions can be found in the literature; here, relying on a result of S. Behrens et al., we present a sufficient condition for the 3-graphicality of a degree sequence and a polynomial time algorithm that realizes one of the associated 3-uniform hypergraphs, if it exists. Both the results are obtained by borrowing some mathematical tools from discrete tomography, a quite recent re- search area involving discrete mathematics, discrete geometry and combinatorics.

BibTeX

@inproceedings {
PFR19,
title="{On the degree sequence of 3-uniform hypergraph}",
author=" C. Picouleau and A. Frosini and S. Rinaldi ",
booktitle="{21 st International Conference on Discrete Geometry for Computer Imagery}",
year=2019,
month="February",
series="LNCS",
pages="to appear",
address=" France",
}