Minimal 4-colored graphs representing an infinite family of hyperbolic 3-manifolds

Paola Cristofori, Evgeny Fominykh, Michele Mulazzani, Vladimir Tarkaev

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


The graph complexity of a compact 3-manifold is defined as the minimum order among all 4-colored graphs representing it. Exact calculations of graph complexity have been already performed, through tabulations, for closed orientable manifolds (up to graph complexity 32) and for compact orientable 3-manifolds with toric boundary (up to graph complexity 12) and for infinite families of lens spaces. In this paper we extend to graph complexity 14 the computations for orientable manifolds with toric boundary and we give two-sided bounds for the graph complexity of tetrahedral manifolds. As a consequence, we compute the exact value of this invariant for an infinite family of such manifolds.

Original languageEnglish
Pages (from-to)781-792
JournalRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Issue number3
StatePublished - 1 Jul 2018
Externally publishedYes

Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology
  • Computational Mathematics
  • Applied Mathematics


  • 3-Manifolds
  • Colored graphs
  • Graph complexity
  • Tetrahedral manifolds


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