Minimal 4-colored graphs representing an infinite family of hyperbolic 3-manifolds. / Cristofori, Paola; Fominykh, Evgeny; Mulazzani, Michele; Tarkaev, Vladimir.
In: Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, Vol. 112, No. 3, 01.07.2018, p. 781-792.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Minimal 4-colored graphs representing an infinite family of hyperbolic 3-manifolds
AU - Cristofori, Paola
AU - Fominykh, Evgeny
AU - Mulazzani, Michele
AU - Tarkaev, Vladimir
N1 - Cristofori, P., Fominykh, E., Mulazzani, M. et al. Minimal 4-colored graphs representing an infinite family of hyperbolic 3-manifolds. RACSAM 112, 781–792 (2018). https://doi.org/10.1007/s13398-017-0478-4
PY - 2018/7/1
Y1 - 2018/7/1
N2 - 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.
AB - 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.
KW - 3-Manifolds
KW - Colored graphs
KW - Graph complexity
KW - Tetrahedral manifolds
UR - http://www.scopus.com/inward/record.url?scp=85049333944&partnerID=8YFLogxK
U2 - 10.1007/s13398-017-0478-4
DO - 10.1007/s13398-017-0478-4
M3 - Article
AN - SCOPUS:85049333944
VL - 112
SP - 781
EP - 792
JO - Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
JF - Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
SN - 1578-7303
IS - 3
ER -
ID: 40112783