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On the Degree Sequences of Uniform Hypergraphs

  • Andrea Frosini
  • Christophe Picouleau
  • Simone Rinaldi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7749)

Abstract

In hypergraph theory, determining a good characterization of d, the degree sequence of an h-uniform hypergraph \(\mathcal{H}\), and deciding the complexity status of the reconstruction of \(\mathcal{H}\) from d, are two challenging open problems. They can be formulated in the context of discrete tomography: asks whether there is a matrix A with nonnegative projection vectors H = (h,h,…,h) and V = (d 1,d 2,…,d n ) with distinct rows.

In this paper we consider the subcase where the vectors H and V are both homogeneous vectors, and we solve the related consistency and reconstruction problems in polynomial time. To reach our goal, we use the concepts of Lyndon words and necklaces of fixed density, and we apply some already known algorithms for their efficient generation.

Keywords

Discrete Tomography Reconstruction problem Lyndon word Necklace hypergraph degree sequence 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Andrea Frosini
    • 1
  • Christophe Picouleau
    • 2
  • Simone Rinaldi
    • 3
  1. 1.Dipartimento di Sistemi e InformaticaUniversitá di FirenzeFirenzeItaly
  2. 2.Laboratoire CEDRICCNAMParisFrance
  3. 3.Dipartimento di Matematica e InformaticaUniversitá di SienaSienaItaly

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