4-colored Graphs and Knot/Link Complements

Paola Cristofori, Evgeny Fominykh, Michele Mulazzani, Vladimir Tarkaev

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


A representation for compact 3-manifolds with non-empty non-spherical boundary via 4-colored graphs (i.e. 4-regular graphs endowed with a proper edge-coloration with four colors) has been recently introduced by two of the authors, and an initial classification of such manifolds has been obtained up to 8 vertices of the representing graphs. Computer experiments show that the number of graphs/manifolds grows very quickly as the number of vertices increases. As a consequence, we have focused on the case of orientable 3-manifolds with toric boundary, which contains the important case of complements of knots and links in the 3-sphere. In this paper we obtain the complete catalogation/classification of these 3-manifolds up to 12 vertices of the associated graphs, showing the diagrams of the involved knots and links. For the particular case of complements of knots, the research has been extended up to 16 vertices.

Original languageEnglish
Pages (from-to)471-490
Number of pages20
JournalResults in Mathematics
Issue number1-2
StatePublished - 1 Sep 2017

Scopus subject areas

  • Mathematics (miscellaneous)
  • Applied Mathematics


  • 3-manifolds
  • Colored graphs
  • Knot/link complements

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