28 citations · 58 across the 23 of their papers we have counts for
23 papers
Pairs of knot invariants
Kouki Taniyama
Let be a map from the set of all knot types to a set . Let be a map from to a set . We define the relation between and to be the…
Crossing numbers and rotation numbers of cycles in a plane immersed graph
Ayumu Inoue, Naoki Kimura, Ryo Nikkuni +1
For any generic immersion of a Petersen graph into a plane, the number of crossing points between two edges of distance one is odd. The sum of the crossing numbers of all -cycle…
Strong and weak (1, 3) homotopies on knot Projections
Noboru Ito, Yusuke Takimura, Kouki Taniyama
Strong and weak (1, 3) homotopies are equivalence relations on knot projections, defined by the first flat Reidemeister move and each of two different types of the third flat Reide…
Circle arrangements of link projections
Noboru Ito, Shosaku Matsuzaki, Kouki Taniyama
An oriented link projection is the image of a generic immersion of oriented circles into the 2-sphere. The circle arrangement of a link projection is a disjoint union of unoriented…
Unknotting numbers and crossing numbers of spatial embeddings of a planar graph
Yuta Akimoto, Kouki Taniyama
It is known that the unknotting number of a link is less than or equal to half the crossing number of . We show that there are a planar graph and its spati…
Knot diagrams on a punctured sphere as a model of string figures
Masafumi Arai, Kouki Taniyama
A string figure is topologically a trivial knot lying on an imaginary plane orthogonal to the fingers with some crossings. The fingers prevent cancellation of these crossings. As a…