Unknotting numbers and crossing numbers of spatial embeddings of a planar graph
Yuta Akimoto, Kouki Taniyama · Journal of Knot Theory and Its Ramifications · 2020
It is known that the unknotting number [Formula: see text] of a link [Formula: see text] is less than or equal to half the crossing number [Formula: see text] of [Formula: see text]. We show that there are a planar graph [Formula: see text] and its spatial embedding [Formula: see text] such that the unknotting number [Formula: see text] of [Formula: see text] is greater than half the crossing number [Formula: see text] of [Formula: see text]. We study relations between unknotting number and crossing number of spatial embedding of a planar graph in general.