28 citations · 100 across the 28 of their papers we have counts for
28 papers
Intrinsic linking of simplicial -complexes in : An additional minimal -complex
Ryo Nikkuni
For any positive integer , the author previously constructed several minimal simplicial -complexes which necessarily contain a non-splittable two-component link, consisting o…
Intrinsic linking of a simplicial -complex embedded in
Ryo Nikkuni
We demonstrate the existence of minimal simplicial -complexes which inevitably contain a nonsplittable two-component link formed by an -sphere and an -sphere in any em…
An intrinsically linked simplicial -complex
Ryo Nikkuni
For any positive integer , Segal--Spież, Lovász--Schrijver, Taniyama and Skopenkov provided examples of simplicial -complexes that inevitably contain a nonsplittable two-comp…
A short proof of the generalized Conway--Gordon--Sachs theorem
Ryo Nikkuni
The famous Conway--Gordon--Sachs theorem for the complete graph on six vertices was extended to the general complete graph on vertices by Kazakov--Korablev as a congruence modu…
Crossing number of graphs and -move
Youngsik Huh, Ryo Nikkuni
The crossing number of a graph is the minimum number of double points over all generic immersions of the graph into the plane. In this paper we investigate the behavior of crossing…
Converses to generalized Conway--Gordon type congruences
Ryo Nikkuni
It is known that for every spatial complete graph on vertices, the summation of the second coefficients of the Conway polynomials over the Hamiltonian knots is congruent t…
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…
Capturing links in spatial complete graphs
Ryo Nikkuni
We say that a set of pairs of disjoint cycles of a graph is linked if for any spatial embedding of there exists an element of such that the -compon…
Generalization of the Conway-Gordon theorem and intrinsic linking on complete graphs
Hiroko Morishita, Ryo Nikkuni
Conway and Gordon proved that for every spatial complete graph on six vertices, the sum of the linking numbers over all of the constituent two-component links is odd, and Kazakov a…
Stick number of non-paneled knotless spatial graphs
Erica Flapan, Kenji Kozai, Ryo Nikkuni
We show that the minimum number of sticks required to construct a non-paneled knotless embedding of is 9 and of is 12 or 13. We use our results about to show that…
Generalizations of the Conway-Gordon theorems and intrinsic knotting on complete graphs
Hiroko Morishita, Ryo Nikkuni
In 1983, Conway and Gordon proved that for every spatial complete graph on six vertices, the sum of the linking numbers over all of the constituent two-component links is odd, and…
Recent Developments in Spatial Graph Theory
Erica Flapan, Thomas Mattman, Blake Mellor +2
This article presents a survey of some recent results in the theory of spatial graphs. In particular, we highlight results related to intrinsic knotting and linking and results abo…
-moves and the difference of Jones polynomials for links
Ryo Nikkuni
The Jones polynomial for an oriented link is a one-variable Laurent polynomial link invariant discovered by Jones. For any integer , we show that: (1) the di…
On calculations of the twisted Alexander ideals for spatial graphs, handlebody-knots and surface-links
Atsushi Ishii, Ryo Nikkuni, Kanako Oshiro
There are many studies about twisted Alexander invariants for knots and links, but calculations of twisted Alexander invariants for spatial graphs, handlebody-knots, and surface-li…
Reduced Wu and Generalized Simon Invariants for Spatial Graphs
Erica Flapan, Will Fletcher, Ryo Nikkuni
We introduce invariants of spatial graphs related to the Wu invariant and the Simon invariant, and apply them to prove that certain graphs are intrinsically chiral, and to obtain l…
A homotopy classification of two-component spatial graphs up to neighborhood equivalence
Atsuhiko Mizusawa, Ryo Nikkuni
A neighborhood homotopy is an equivalence relation on spatial graphs which is generated by crossing changes on the same component and neighborhood equivalence. We give a complete c…
Conway-Gordon type theorem for the complete four-partite graph
Hiroka Hashimoto, Ryo Nikkuni
We give a Conway-Gordon type formula for invariants of knots and links in a spatial complete four-partite graph in terms of the square of the linking number and the s…
On Conway-Gordon type theorems for graphs in the Petersen family
Hiroka Hashimoto, Ryo Nikkuni
For every spatial embedding of each graph in the Petersen family, it is known that the sum of the linking numbers over all of the constituent 2-component links is congruent to 1 mo…
-exchanges and the Conway-Gordon theorems
Ryo Nikkuni, Kouki Taniyama
Conway-Gordon proved that for every spatial complete graph on 6 vertices, the sum of the linking numbers over all of the constituent 2-component links is congruent to 1 modulo 2, a…
On intrinsically knotted or completely 3-linked graphs
Ryo Hanaki, Ryo Nikkuni, Kouki Taniyama +1
We say that a graph is intrinsically knotted or completely 3-linked if every embedding of the graph into the 3-sphere contains a nontrivial knot or a 3-component link any of whose…
A refinement of the Conway-Gordon theorems
Ryo Nikkuni
In 1983, Conway-Gordon showed that for every spatial complete graph on 6 vertices, the sum of the linking numbers over all of the constituent 2-component links is congruent to 1 mo…
On the Wu invariants for immersions of a graph into the plane
Ryo Nikkuni
We give an explicit calculation of the Wu invariants for immersions of a finite graph into the plane and classify all generic immersions of a graph into the plane up to regular hom…
Regular projections of graphs with at most three double points
Youngsik Huh, Ryo Nikkuni
A generic immersion of a planar graph into the 2-space is said to be knotted if there does not exist a trivial embedding of the graph into the 3-space obtained by lifting the immer…
An intrinsic non-triviality of graphs
Ryo Nikkuni
We say that a graph is intrinsically non-trivial if every spatial embedding of the graph contains a non-trivial spatial subgraph. We prove that an intrinsically non-trivial graph i…