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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

Harvard

Cristofori, P, Fominykh, E, Mulazzani, M & Tarkaev, V 2018, 'Minimal 4-colored graphs representing an infinite family of hyperbolic 3-manifolds', Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, vol. 112, no. 3, pp. 781-792. https://doi.org/10.1007/s13398-017-0478-4

APA

Cristofori, P., Fominykh, E., Mulazzani, M., & Tarkaev, V. (2018). Minimal 4-colored graphs representing an infinite family of hyperbolic 3-manifolds. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, 112(3), 781-792. https://doi.org/10.1007/s13398-017-0478-4

Vancouver

Cristofori P, Fominykh E, Mulazzani M, Tarkaev V. Minimal 4-colored graphs representing an infinite family of hyperbolic 3-manifolds. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas. 2018 Jul 1;112(3):781-792. https://doi.org/10.1007/s13398-017-0478-4

Author

Cristofori, Paola ; Fominykh, Evgeny ; Mulazzani, Michele ; Tarkaev, Vladimir. / Minimal 4-colored graphs representing an infinite family of hyperbolic 3-manifolds. In: Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas. 2018 ; Vol. 112, No. 3. pp. 781-792.

BibTeX

@article{94e4b08fe3e1430ab94f57f74e8f26a8,
title = "Minimal 4-colored graphs representing an infinite family of hyperbolic 3-manifolds",
abstract = "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.",
keywords = "3-Manifolds, Colored graphs, Graph complexity, Tetrahedral manifolds",
author = "Paola Cristofori and Evgeny Fominykh and Michele Mulazzani and Vladimir Tarkaev",
note = "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",
year = "2018",
month = jul,
day = "1",
doi = "10.1007/s13398-017-0478-4",
language = "English",
volume = "112",
pages = "781--792",
journal = "Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas",
issn = "1578-7303",
publisher = "Springer Nature",
number = "3",

}

RIS

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