Minimal arc-presentations of some nonalternating knots
type: Item
instance of: scholarly article
title: Minimal arc-presentations of some nonalternating knots
zbMATH Open document ID: 0913.57007
DOI: 10.1016/S0166-8641(97)00024-2
author: Elisabetta Beltrami
author: Peter R. Cromwell
published in: Topology and its Applications
publication date: 1999-05-31T00:00:00Z
review text: The authors construct arc-presentations of special links and prove the minimality of the arc indices of these. The diagrams of the links considered are sums of strongly alternating tangle diagrams, but not alternating themselves. The construction is only applicable, if a certain graph derived from the diagram contains a certain Hamiltonian path -- for which a general condition cannot be given. Minimality is proved by an unequality connecting the arc index with the Kauffman polynomial of the link, a new result due to H. R. Morton and the first author.
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 1140213
zbMATH Keywords: arc-presentation
zbMATH Keywords: mutation
zbMATH Keywords: Kauffman polynomial
reviewed by: Gerhard Burde
MaRDI profile type: Publication
cites work: Special positions for essential tori in link complements
cites work: A theorem on paths in planar graphs
cites work: Embedding knots and links in an open book. I: Basic properties
cites work: Q3840290
cites work: Embedding knots and links in an open book II. Bounds on arc index
cites work: Some links with non-trivial polynomials and their crossing-numbers
cites work: Arc index and the Kauffman polynomial
cites work: Embedding knots and links in an open book III. On the braid index of satellite links
cites work: ARC Index and the Kauffman Polynomial
cites work: Q4107635
cites work: On the Kauffman polynomial of an adequate link
description: scientific article; zbMATH DE number 1140213