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.
U2 - 10.48550/arXiv.1904.03117
DO - 10.48550/arXiv.1904.03117
M3 - Report
VL - 1904.03117v2
T3 - cs.DS
BT - Knot Diagrams of Treewidth Two
PB - Cornell University - arXiv
CY - Cornell University Library, US
ER -