Embedding knots and links in an open book II. Bounds on arc index

DOI10.1017/S0305004100074181zbMath0860.57007MaRDI QIDQ4877663

Ian J. Nutt, Peter R. Cromwell

Publication date: 21 April 1997

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

zbMATH Keywords

knots3-spherelinkscrossing numberopen-book decompositionarc indexarc presentations

Mathematics Subject Classification ID

Related Items (18)

Spatial graph as connected sum of a planar graph and a braid ⋮ On the arc index of cable links and Whitehead doubles ⋮ Embedding knots and links in an open book. I: Basic properties ⋮ Arc index via the alternating tangle decomposition ⋮ Prime knots with arc index 12 up to 16 crossings ⋮ Bisected vertex leveling of plane graphs: Braid index, arc index and delta diagrams ⋮ Minimal arc-presentations of some nonalternating knots ⋮ A polynomial upper bound on Reidemeister moves ⋮ PRIME KNOTS WITH ARC INDEX UP TO 11 AND AN UPPER BOUND OF ARC INDEX FOR NON-ALTERNATING KNOTS ⋮ Arc index of pretzel knots of type (-𝑝,𝑞,𝑟) ⋮ THE PROBLEM OF DETECTING THE SATELLITE STRUCTURE OF A LINK BY MONOTONIC SIMPLIFICATION ⋮ Three-page approach to knot theory. Encoding and local moves ⋮ A TABULATION OF PRIME KNOTS UP TO ARC INDEX 11 ⋮ A circular embedding of a graph in Euclidean 3-space ⋮ Three-page approach to knot theory. Universal semigroup ⋮ On the arc index of an adequate link ⋮ THREE-PAGE ENCODING AND COMPLEXITY THEORY FOR SPATIAL GRAPHS ⋮ ON THE PRESENTATION OF A LINK AS A SUM OF TWO DESCENDING TANGLE DIAGRAMS

Cites Work

• A spanning tree expansion of the Jones polynomial
• State models and the Jones polynomial
• Jones polynomials and classical conjectures in knot theory
• Special positions for essential tori in link complements
• A Theorem on Planar Graphs
• Hamiltonian circuits on 3-polytopes

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