16 citations · 36 across the 11 of their papers we have counts for
13 papers
Classification of (uncolored) bonded knots and links
Boštjan Gabrovšek, Matic Simonič, Wanda Niemyska
We present a systematic classification of uncolored bonded knots with singularity number at most seven. Bonded knots provide a topological model for closed protein chains with intr…
A table of knotoids in up to seven crossings
Boštjan Gabrovšek, Paolo Cavicchioli
We present a complete classification of spherical knotoids with up to six crossings and conjecture that our classification up to seven crossings is complete. Our work extends the t…
Bonded braids and the Markov theorem
Paolo Cavicchioli, Boštjan Gabrovšek, Matic Simonič
Bonded knots arise naturally in topological protein modeling, where intramolecular interactions such as disulfide bridges stabilize folded configurations. These structures extend c…
Classification of algebraic tangles
Bartosz Ambrozy Gren, Joanna Ida Sulkowska, Boštjan Gabrovšek
We study algebraic tangles as fundamental components in knot theory, developing a systematic approach to classify and tabulate prime tangles using a novel canonical representation.…
The bracket polynomial of bonded knots and applications to entangles proteins
Boštjan Gabrovšek, Matic Simonič
We model proteins with intramolecular bonds, such as disulfide bridges, using the concept of bonded knots -- closed loops in three-dimensional space equipped with additional bonds…
A fresh look to a randomized massively parallel graph coloring algorithm
Boštjan Gabrovšek, Janez Žerovnik
Petford and Welsh introduced a sequential heuristic algorithm for (approximately) solving the NP-hard graph coloring problem. The algorithm is based on the antivoter model and mimi…
An invariant for colored bonded knots
Bostjan Gabrovsek
We equip a knot with a set of colored bonds, that is, colored intervals properly embedded into . Such a construction can be viewed as a structure that…
The Alexander polynomial for closed braids in lens spaces
Boštjan Gabrovšek, Eva Horvat
We present a reduced Burau-like representation for the mixed braid group on one strand representing links in lens spaces and show how to calculate the Alexander polynomial of a lin…
Knot invariants in lens spaces
Boštjan Gabrovšek, Eva Horvat
In this survey we summarize results regarding the Kauffman bracket, HOMFLYPT, Kauffman 2-variable and Dubrovnik skein modules, and the Alexander polynomial of links in lens spaces,…
Link diagrams in Seifert manifolds and applications to skein modules
Boštjan Gabrovšek, Maciej Mroczkowski
In this survey paper we present results about link diagrams in Seifert manifolds using arrow diagrams, starting with link diagrams in and , where $F…
A Markov theorem for generalized plat decomposition
Alessia Cattabriga, Boštjan Gabrovšek
We prove a Markov theorem for tame links in a connected closed orientable 3-manifold with respect to a plat-like representation. More precisely, given a genus Heegaard surf…
Tabulation of prime knots in lens spaces
Boštjan Gabrovšek
Using computational techniques we tabulate prime knots up to five crossings in the solid torus and the infinite family of lens spaces . For these knots we calculate the sec…
On the Alexander polynomial of links in lens spaces
Eva Horvat, Boštjan Gabrovšek
We show how the Alexander polynomial of links in lens spaces is related to the classical Alexander polynomial of a link in the 3-sphere, obtained by cutting out the exceptional len…