Families of Metrized Graphs with Small Tau Constants


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ÇINKIR Z.

ANNALS OF COMBINATORICS, cilt.20, ss.317-344, 2016 (SCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 20 Konu: 2
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1007/s00026-016-0304-2
  • Dergi Adı: ANNALS OF COMBINATORICS
  • Sayfa Sayısı: ss.317-344

Özet

Baker and Rumely's tau lower bound conjecture claims that if the tau constant of a metrized graph is divided by its total length, this ratio must be bounded below by a positive constant for all metrized graphs. We construct several families of metrized graphs having small tau constants. In addition to numerical computations, we prove that the tau constants of the metrized graphs in one of these families, the hexagonal nets around a torus, asymptotically approach to 108 which is our conjectural lower bound.