Topology Atlas | Conferences

Knots in Washington XXXV
December 7-9, 2012
George Washington University
Washington, DC, USA

Organizers
Mieczyslaw K. Dabkowski (UT Dallas), Valentina Harizanov (GWU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Radmila Sazdanovic (U.Penn), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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The pallet graph of a Fox coloring
by
Shin Satoh
Kobe University
Coauthors: Takuji Nakamura and Yasutaka Nakanishi

We introduce the notion of a graph associated with a Fox p-coloring of a knot, and prove that any non-trivial p-coloring requires at least [log_2 p]+2 colors. Moreover, we also prove that this lower bound is best possible in the sense that there is a p-colorable virtual knot which attains the bound.

Date received: October 23, 2012

Copyright © 2012 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 # cbfw-07.