# Tagged Questions

**10**

votes

**2**answers

487 views

### Is every knot unavoidable in the embeddings of some graph?

Is it the case that, for any given knot $K$,
there exists some graph $G$ whose every embedding into $\mathbb{R}^3$
(or into $\mathbb{S}^3$)
contains a cycle that realizes $K$?
I know the ...

**2**

votes

**1**answer

192 views

### Min Bend Orthogonal Knots

I am seeking literature on 3D orthogonal drawings of knots,
especially minimum bend drawings.
An orthogonal drawing employs segments parallel to the axes of
a Cartesian coordinate system.
A bend is a ...

**26**

votes

**1**answer

1k views

### Does this knot invariant distinguish trefoil chiralities?

Let $C_N$ denote the labelled configuration of $N^{th}$ roots of unity with $p_J = e^{\frac{2\pi iJ}{N}}$ for $J = 1\ldots N$.
As a corollary of something else I was playing around with, I recently ...

**17**

votes

**7**answers

2k views

### Is there a “knot theory” for graphs?

I think knot theory has been studied for quite a while (like a century or so), so I'm just wondering whether there is a "knot theory" for graphs, i.e. the study of (topological properties of) ...

**1**

vote

**2**answers

345 views

### Untangling a graph

Assume you have a 4-valent graph (i.e., a knot universe, i.e. a collection
of self-intersecting curves). Your allowed moves are the equivalents
of Reidemeister 1, 2, 3, just with 4-nodes instead of ...

**0**

votes

**1**answer

231 views

### “Skein” equations sets that can reduce any graph

Consider for example the approach to the Kuperberg G2 or the Yamada polynomial. I don't know whether relations of graph (in contrast to knot) theory are also usually called "skein" but
I simply carry ...

**2**

votes

**2**answers

998 views

### How many lanes has a freeway? (Crossing free Kuperberg G2, that is.) EDITED

For referencing, I keep the original title and post and ask
only about the simplest case (and forget the freeway with crossings
for now).
Consider a trivalent graph, e.g. the dodecahedron or cube ...

**3**

votes

**0**answers

287 views

### Computing Quantum Dimensions

Hi,
in "Jaegerâ€™s Higman-Sims state model and the B2 spider" by Greg Kuperberg
(arxiv:math9601221v1, 1996) there are some quantum dimensions listed in the
"Discussion" part. Evidently quantum groups ...