12 papers
Fox -Colorings as Fixed Points of Braid Representations
Neungjoo Goh, Suah Jeong, Seungbin Oh +1
Fox -colorings of knots and links admit a linear-algebraic description in terms of braid representations. For each braid we associate a representation $M : B_n \to \m…
A diagrammatic approach to the three-page index
Hyungkee Yoo
The three-page index is an invariant that measures the complexity of representing a link in a three-page book. It is known that admits a linear upper bound in…
New Upper Bounds on the Ribbonlength of Alternating Links with Bipartite Dual Graphs
Hyungkee Yoo
The ribbonlength of a link is a geometric invariant defined as the infimum of the ratio of the length to the width of a folded ribbon realization of the link. In this paper, we pro…
Three-page indices of torus links
Useong Jang, Minseo Lee, Hyungkee Yoo
An arc presentation of a link is an embedding into the open book decomposition of with a finite number of pages. An important rule of arc presentations is that diffe…
Linear Upper Bounds on the Ribbonlength of Knots and Links
Hyoungjun Kim, Sungjong No, Hyungkee Yoo
A knotted ribbon is one of physical aspect of a knot. A folded ribbon knot is a depiction of a knot obtained by folding a long and thin rectangular strip to become flat. The ribbon…
Linking numbers of Montesinos links
Hyoungjun Kim, Sungjong No, Hyungkee Yoo
The linking number of an oriented two-component link is an invariant indicating how intertwined the two components are. Tuler proved that the linking number of a two-component rati…
On the Laplacian spectrum of -symmetric graphs
Sunyo Moon, Hyungkee Yoo
For some positive integer , if the finite cyclic group can act freely on a graph , then we say that is -symmetric. In 1985, Faria showed that the multip…
Petal number of torus knots using superbridge indices
Hyoungjun Kim, Sungjong No, Hyungkee Yoo
A petal projection of a knot is a projection of a knot which consists of a single multi-crossing and non-nested loops. Since a petal projection gives a sequence of natural numb…
Ribbonlength of twisted torus knots
Hyoungjun Kim, Sungjong No, Hyungkee Yoo
The ribbonlength Rib of a knot is the infimum of the ratio of the length of any flat knotted ribbon with core to its width. A twisted torus knot is obtai…
Folded ribbonlength of 2-bridge knots
Hyoungjun Kim, Sungjong No, Hyungkee Yoo
A ribbon is a two-dimensional object with one-dimensional properties which is related with geometry, robotics and molecular biology. A folded ribbon structure provides a complex st…
Lattice stick number of spatial graphs
Hyungkee Yoo, Chaeryn Lee, Seungsang Oh
The lattice stick number of knots is defined to be the minimal number of straight sticks in the cubic lattice required to construct a lattice stick presentation of the knot. We sim…
Bisected vertex leveling of plane graphs: braid index, arc index and delta diagrams
Sungjong No, Seungsang Oh, Hyungkee Yoo
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 mi…