A representation for compact 3-manifolds with non-empty nonspherical 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 classication 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/classication 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.

4-colored graphs and knot/link complements / Cristofori, Paola; Fominykh, Evgeny; Mulazzani, Michele; Tarkaev, Vladimir. - In: RESULTS IN MATHEMATICS. - ISSN 1422-6383. - 72:1-2(2017), pp. 471-490. [10.1007/s00025-017-0686-4]

4-colored graphs and knot/link complements

CRISTOFORI, Paola;
2017

Abstract

A representation for compact 3-manifolds with non-empty nonspherical 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 classication 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/classication 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.
2017
23-mag-2017
72
1-2
471
490
4-colored graphs and knot/link complements / Cristofori, Paola; Fominykh, Evgeny; Mulazzani, Michele; Tarkaev, Vladimir. - In: RESULTS IN MATHEMATICS. - ISSN 1422-6383. - 72:1-2(2017), pp. 471-490. [10.1007/s00025-017-0686-4]
Cristofori, Paola; Fominykh, Evgeny; Mulazzani, Michele; Tarkaev, Vladimir
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1132669
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