Topology Atlas | Conferences

Knots in Washington XXXVII
January 19-20, 2014
George Washington University
Washington, DC, USA

Mieczyslaw K. Dabkowski (UT Dallas), Valentina Harizanov (GWU), Jozef H. Przytycki (GWU and UMCP), Yongwu Rong (GWU), Radmila Sazdanovic (NCSU), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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Effective 9-colorings for knots
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.