" Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics.
This enyclopedia is filled with valuable information on a rich and fascinating subject."–Ed …

In this paper, we obtain the necessary and sufficient condition that two knot projections are
related by a finite sequence of the first and second flat Reidemeister moves (Theorem 2.2) …

An increasing sequence of integers is said to be universal for knots and links if every knot
and link has a reduced projection on the sphere such that the number of edges of each …

It is well known that there is a one-to-one correspondence between signed plane graphs
and link diagrams via the medial construction. The component number of the corresponding …

arXiv:0905.2478v1 [math.CO] 15 May 2009 Page 1 arXiv:0905.2478v1 [math.CO] 15 May 2009
The Link Component Number of Suspended Trees Toshiki Endo Jiyu Gakuen College, 1-8-15 …

A triple chord fis a sub-diagram of a chord diagram that consists of a circle and finitely many
chords connecting the preimages for every double point on a spherical curve. This paper …

When drawing planar representations of mathematical knots, it is challenging to find 2D
embeddings that minimise the amount of smoothing required to produce aesthetically …

A link diagram is said to be lune-free if, when viewed as a 4-regular plane graph it does not
have multiple edges between any pair of nodes. We prove that any colored link diagram is …

In this paper, we introduce a bisected vertex leveling of a plane graph. Using this planar
embedding, we present elementary proofs of the well-known upper bounds in terms of the …