Translator Disclaimer
VOL. 55 | 2009 A table of $\theta$-curves and handcuff graphs with up to seven crossings
Hiromasa Moriuchi

Editor(s) Jean-Pierre Bourguignon, Motoko Kotani, Yoshiaki Maeda, Nobuyuki Tose

Abstract

We enumerate all the $\theta$-curves and handcuff graphs with up to seven crossings by using algebraic tangles and prime basic $\theta$-polyhedra. Here, a $\theta$-polyhedron is a connected graph embedded in a 2-sphere, whose two vertices are 3-valent, and the rest are 4-valent. There exist twenty-four prime basic $\theta$-polyhedra with up to seven 4-valent vertices. We can obtain a $\theta$-curve and handcuff graph diagram from a prime basic $\theta$-polyhedron by substituting algebraic tangles for their 4-valent vertices.

Information

Published: 1 January 2009
First available in Project Euclid: 28 November 2018

zbMATH: 1179.57004
MathSciNet: MR2463504

Digital Object Identifier: 10.2969/aspm/05510281

Rights: Copyright © 2009 Mathematical Society of Japan

PROCEEDINGS ARTICLE
10 PAGES


SHARE
Back to Top