10 citations · 44 across the 12 of their papers we have counts for
18 papers
Computing distances in braid-move graphs, higher Bruhat orders, and oriented-matroid mutation graphs is NP-hard
Tilen Marc
A reduced word of the longest permutation , taken up to commutations, encodes a wiring diagram of pseudolines, and a braid move $σ_iσ_{i+1}σ_i\leftrightarrowσ_{i+1}…
Edge-Isoperimetric Inequalities in Chamber Graphs of Hyperplane Arrangements
Tilen Marc
We study edge-isoperimetric inequalities in chamber graphs of affine hyperplane arrangements. Our approach is topological: to a set of chambers we associate its thickening in Eucli…
Unlabeled sample compression schemes for oriented matroids
Tilen Marc
A long-standing sample compression conjecture asks to linearly bound the size of the optimal sample compression schemes by the Vapnik-Chervonenkis (VC) dimension of an arbitrary cl…
Corners and simpliciality in oriented matroids and partial cubes
Kolja Knauer, Tilen Marc
Building on a recent characterization of tope graphs of Complexes of Oriented Matroids (COMs), we tackle and generalize several classical problems in Oriented Matroids (OMs), Lopsi…
On graphs with equal total domination and Grundy total domination number
Tanja Gologranc, Marko Jakovac, Tim Kos +1
A sequence of vertices in a graph without isolated vertices is called a total dominating sequence if every vertex in the sequence totally dominates at…
On the Djoković-Winkler relation and its closure in subdivisions of fullerenes, triangulations, and chordal graphs
Sandi Klavžar, Kolja Knauer, Tilen Marc
It was recently pointed out that certain SiO layer structures and SiO nanotubes can be described as full subdivisions aka subdivision graphs of partial cubes. A key tool fo…