12 citations · 45 across the 25 of their papers we have counts for
28 papers
Four triangle-free intrinsically knotted graphs with 22 edges
Hyoungjun Kim, Thomas W. Mattman, Seungsang Oh
An intrinsically knotted graph is one for which every spatial embedding contains a nontrivially knotted cycle. Classifying such graphs is a central problem in spatial graph theory.…
Bipartite intrinsically knotted graphs with 23 edges
Hyoungjun Kim, Thomas W Mattman, Seungsang Oh
A graph is intrinsically knotted if every embedding contains a nontrivially knotted cycle. It is known that intrinsically knotted graphs have at least 21 edges and that there are e…
State matrix recursion method and monomer--dimer problem
Seungsang Oh
The exact enumeration of pure dimer coverings on the square lattice was obtained by Kasteleyn, Temperley and Fisher in 1961. In this paper, we consider the monomer-dimer covering p…
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…
Bounds on multiple self-avoiding polygons
Kyungpyo Hong, Seungsang Oh
A self-avoiding polygon is a lattice polygon consisting of a closed self-avoiding walk on a square lattice. Surprisingly little is known rigorously about the enumeration of self-av…