TY - BOOK

T1 - Knot Diagrams of Treewidth Two

AU - Bodlaender, H.L.

AU - Burton, Benjamin

AU - Fomin, Fedor

AU - Grigoriev, Alexander

N1 - data source: NO DATA USED

PY - 2019/4/8

Y1 - 2019/4/8

N2 - In this paper, we study knot diagrams for which the underlying graph has treewidth two. We give a linear time algorithm for the following problem: given a knot diagram of treewidth two, does it represent the unknot? We also show that for a link diagram of treewidth two we can test in linear time if it represents the unlink. From the algorithm, it follows that a diagram of the unknot of treewidth 2 can always be reduced to the trivial diagram with at most n (un)twist and (un)poke Reidemeister moves.

AB - In this paper, we study knot diagrams for which the underlying graph has treewidth two. We give a linear time algorithm for the following problem: given a knot diagram of treewidth two, does it represent the unknot? We also show that for a link diagram of treewidth two we can test in linear time if it represents the unlink. From the algorithm, it follows that a diagram of the unknot of treewidth 2 can always be reduced to the trivial diagram with at most n (un)twist and (un)poke Reidemeister moves.

M3 - Report

VL - 1904.03117v2

T3 - cs.DS

BT - Knot Diagrams of Treewidth Two

PB - arXiv.org at Cornell University Library

CY - Cornell University Library, US

ER -