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On the Degree Sequence of 3-Uniform Hypergraph: A New Sufficient Condition

  • Andrea FrosiniEmail author
  • Christophe Picouleau
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11414)

Abstract

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 \(\pi =(d_1,d_2,\ldots ,d_n)\) a non increasing sequence of positive integers, is \(\pi \) the degree sequence of a h-uniform simple hypergraph?

Now, assuming \(P\ne NP\), 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 research area involving discrete mathematics, discrete geometry and combinatorics.

Keywords

h-uniform hypergraph Hypergraph degree sequence Discrete tomography Reconstruction problem 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversità di FirenzeFlorenceItaly
  2. 2.CEDRIC, CNAMParis Cedex 03France

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