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Effective 9-colorings for knots
by
Shin Satoh
Kobe University
Coauthors: Yasutaka Nakanishi and Takuji Nakamura
For a composite odd integer n¥geq 9, we introduce the notion of an effective n-coloring for a 1- or 2-dimensional knots and give a lower bound for the minimal number of colors for all effective n-colorings. In particular, we prove that any effectively 9-colorable 1- or 2-knot is presented by some diagram where exactly five colors of nine are assigned to the arcs or sheets.
Date received: January 7, 2014
Copyright © 2014 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbid-20.