Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 26 min ago
PreprintarXiv licencearXiv

Matroids and isomorphism problems for Bestvina-Brady groups

  • Yu-Chan Chang
  • Lorenzo Ruffoni
Open at sourcePDFDOICite

Abstract

We propose a factorization of the graph isomorphism problem for Bestvina-Brady groups (BBGs) through matroid theory. In particular, we show that finitely presented BBGs depend on their defining graphs only through their cycle matroids. On the other hand, we construct graphs of arbitrarily high connectivity such that they have non-isomorphic cycle matroids but their BBGs are isomorphic. To do so, we prove that if a graph admits a tree clique-spanner, then the Dicks-Leary presentation of its BBG can be explicitly simplified to a right-angled Artin group presentation. In particular, we show that BBGs defined by dually chordal graphs are right-angled Artin groups.

Related

  1. Conjugator length of Bestvina-Brady groups
    Jerónimo García-Mejía, Matteo Migliorini
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Large profinite genus and extensions in Bestvina-Brady groups
    Vladimir Vankov
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. The Euler Characteristic of Spherical Bestvina-Brady Kernels
    Eduardo Flores Martínez
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  4. On the complexity of isomorphism problems for tensors, groups, and polynomials V: over commutative rings
    Joshua A. Grochow, Youming Qiao, Katherine E. Stange +1
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. The Codegree Isomorphism Conjecture for Finite Simple Groups
    Yong Yang
    arXivPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{chang2026matroids,
  title = {{Matroids and isomorphism problems for Bestvina-Brady groups}},
  author = {Yu-Chan Chang and Lorenzo Ruffoni},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.16345},
  eprint = {2609.16345},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16345},
}
RIS
TY  - UNPB
TI  - Matroids and isomorphism problems for Bestvina-Brady groups
AU  - Yu-Chan Chang
AU  - Lorenzo Ruffoni
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.16345
UR  - https://arxiv.org/abs/2609.16345
AB  - We propose a factorization of the graph isomorphism problem for Bestvina-Brady groups (BBGs) through matroid theory. In particular, we show that finitely presented BBGs depend on their defining graphs only through their cycle matroids. On the other hand, we construct graphs of arbitrarily high connectivity such that they have non-isomorphic cycle matroids but their BBGs are isomorphic. To do so, we prove that if a graph admits a tree clique-spanner, then the Dicks-Leary presentation of its BBG can be explicitly simplified to a right-angled Artin group presentation. In particular, we show that BBGs defined by dually chordal graphs are right-angled Artin groups.
ER  -