Minimal 4-colored graphs representing an infinite family of hyperbolic 3-manifolds

作者：Cristofori Paola; Fominykh Evgeny; Mulazzani Michele^*; Tarkaev Vladimir

来源：Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales Serie A-Matematicas, 2018, 112(3): 781-792.

DOI：10.1007/s13398-017-0478-4

• 3-Manifolds
• Colored graphs
• Graph complexity
• Tetrahedral manifolds

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.

• 出版日期2018-7