THE PLANARITY PROBLEM II

Author:

CAIRNS GRANT1,ELTON DANIEL M.1

Affiliation:

1. Department of Mathematics, La Trobe University, Melbourne, Australia 3083, Australia

Abstract

C.F. Gauss gave a necessary condition for a word to be the intersection sequence of a closed normal planar curve and he gave an example which showed that his condition was not sufficient. Since then several authors have given algorithmic solutions to this problem. In a previous paper, along the lines of Gauss’s original condition, we gave a necessary and sufficient condition for the planarity of “signed” Gauss words. In this present paper we give a solution to the planarity problem for unsigned Gauss words.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Cited by 21 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Describing realizable Gauss diagrams using the concepts of parity or bipartite graphs;Journal of Knot Theory and Its Ramifications;2023-09

2. Gauss-Lintel, an Algorithm Suite for Exploring Chord Diagrams;Lecture Notes in Computer Science;2021

3. On realizabilty of Gauss diagrams and constructions of meanders;Journal of Knot Theory and Its Ramifications;2020-04

4. Picture-valued parity-biquandle bracket;Journal of Knot Theory and Its Ramifications;2020-02

5. Parity conditions for realizability of Gauss diagrams;Journal of Knot Theory and Its Ramifications;2019-01

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