On the graph labellings arising from phylogenetics

Weronika Buczyńska; Jarosław Buczyński; Kaie Kubjas; Mateusz Michałek

Open Mathematics (2013)

  • Volume: 11, Issue: 9, page 1577-1592
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Weronika Buczyńska, et al. "On the graph labellings arising from phylogenetics." Open Mathematics 11.9 (2013): 1577-1592. <http://eudml.org/doc/269753>.

@article{WeronikaBuczyńska2013,
abstract = {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.},
author = {Weronika Buczyńska, Jarosław Buczyński, Kaie Kubjas, Mateusz Michałek},
journal = {Open Mathematics},
keywords = {Graph labellings; Phylogenetic semigroup; Semigroup generators; Lattice cone; Hilbert basis; Conformal block algebras; Cavender-Farris-Neyman model; 2-state Jukes-Cantor model; graph labellings; phylogenetic semigroup; semigroup generators; lattice cone; conformal block algebras},
language = {eng},
number = {9},
pages = {1577-1592},
title = {On the graph labellings arising from phylogenetics},
url = {http://eudml.org/doc/269753},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Weronika Buczyńska
AU - Jarosław Buczyński
AU - Kaie Kubjas
AU - Mateusz Michałek
TI - On the graph labellings arising from phylogenetics
JO - Open Mathematics
PY - 2013
VL - 11
IS - 9
SP - 1577
EP - 1592
AB - 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.
LA - eng
KW - Graph labellings; Phylogenetic semigroup; Semigroup generators; Lattice cone; Hilbert basis; Conformal block algebras; Cavender-Farris-Neyman model; 2-state Jukes-Cantor model; graph labellings; phylogenetic semigroup; semigroup generators; lattice cone; conformal block algebras
UR - http://eudml.org/doc/269753
ER -

References

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