Central European Journal of Mathematics

, Volume 11, Issue 9, pp 1577–1592 | Cite as

On the graph labellings arising from phylogenetics

  • Weronika Buczyńska
  • Jarosław Buczyński
  • Kaie Kubjas
  • Mateusz Michałek
Research Article


We study semigroups of labellings associated to a graph. These generalise the Jukes-Cantor model and phylogenetic toric varieties defined in [Buczynska W., Phylogenetic toric varieties on graphs, J. Algebraic Combin., 2012, 35(3), 421–460]. Our main theorem bounds the degree of the generators of the semigroup by g + 1 when the graph has first Betti number g. Also, we provide a series of examples where the bound is sharp.


Graph labellings Phylogenetic semigroup Semigroup generators Lattice cone Hilbert basis Conformal block algebras Cavender-Farris-Neyman model 2-state Jukes-Cantor model 


20M14 14M25 20M05 52B20 13P25 14D21 


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Copyright information

© Versita Warsaw and Springer-Verlag Wien 2013

Authors and Affiliations

  • Weronika Buczyńska
    • 1
  • Jarosław Buczyński
    • 1
  • Kaie Kubjas
    • 2
  • Mateusz Michałek
    • 1
    • 3
  1. 1.Institute of Mathematics of the Polish Academy of SciencesWarsawPoland
  2. 2.Institut für MathematikFreie Universität BerlinBerlinGermany
  3. 3.Max Planck Institute for MathematicsBonnGermany

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