TY - JOUR

T1 - 4-colored Graphs and Knot/Link Complements

AU - Cristofori, Paola

AU - Fominykh, Evgeny

AU - Mulazzani, Michele

AU - Tarkaev, Vladimir

PY - 2017/9/1

Y1 - 2017/9/1

N2 - 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.

AB - 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.

KW - 3-manifolds

KW - Colored graphs

KW - Knot/link complements

UR - http://www.scopus.com/inward/record.url?scp=85019846760&partnerID=8YFLogxK

U2 - 10.1007/s00025-017-0686-4

DO - 10.1007/s00025-017-0686-4

M3 - Article

AN - SCOPUS:85019846760

VL - 72

SP - 471

EP - 490

JO - Results in Mathematics

JF - Results in Mathematics

SN - 1422-6383

IS - 1-2

ER -