Final published version
Research output: Other contribution
Research output: Other contribution
}
TY - GEN
T1 - The incompatibility of crossing number and bridge number for knot diagrams Appendix. A note on Wirtinger number and flypes by Ryan Blair and Nathaniel Morrison
AU - Blair, Ryan
AU - Ozawa, Makoto
AU - Kjuchukova, Alexandra
AU - Morrison, Nathaniel
N1 - I helped author the appendix to this article, “A note on Wirtinger number and flypes,” rather than the main article. My name therefore appears above the appendix instead of in the main author line.
PY - 2019/7/1
Y1 - 2019/7/1
N2 - We study methods for computing the bridge number of a knot from a knot diagram. We prove equivalence between a geometric and a combinatorial definition of the bridge number of a knot diagram. For each notion of diagrammatic bridge number considered, we find crossing number minimizing knot diagrams which fail to minimize bridge number. Furthermore, we construct a family of minimal crossing diagrams for which the difference between diagrammatic bridge number and the actual bridge number of the knot grows to infinity.
AB - We study methods for computing the bridge number of a knot from a knot diagram. We prove equivalence between a geometric and a combinatorial definition of the bridge number of a knot diagram. For each notion of diagrammatic bridge number considered, we find crossing number minimizing knot diagrams which fail to minimize bridge number. Furthermore, we construct a family of minimal crossing diagrams for which the difference between diagrammatic bridge number and the actual bridge number of the knot grows to infinity.
U2 - 10.1016/j.disc.2019.03.013
DO - 10.1016/j.disc.2019.03.013
M3 - Other contribution
VL - 342
T3 - Discrete Mathematics
PB - Elsevier
ER -