5 citations · 5 across the 7 of their papers we have counts for
9 papers
Local version of Vizing's theorem for multi-graphs
Clinton T. Conley, Jan Grebik, Oleg Pikhurko
Extending a result of Christiansen, we prove that every mutli-graph admits a proper edge colouring which is local, that is, $ϕ(e)\le \max\{d(x)+π(x…
On Homomorphism Graphs
Sebastian Brandt, Yi-Jun Chang, Jan Grebík +3
We introduce a new type of examples of bounded degree acyclic Borel graphs and study their combinatorial properties in the context of descriptive combinatorics, using a generalizat…
Approximate Schreier decorations and approximate Kőnig's line coloring Theorem
Jan Grebik
Following recent result of L. M. T\' oth [arXiv:1906.03137] we show that every -regular Borel graph with a (not necessarily invariant) Borel probability measure a…
Local Problems on Trees from the Perspectives of Distributed Algorithms, Finitary Factors, and Descriptive Combinatorics
Sebastian Brandt, Yi-Jun Chang, Jan Grebík +3
We study connections between distributed local algorithms, finitary factors of iid processes, and descriptive combinatorics in the context of regular trees. We extend the Borel det…
-Lacunary actions of Polish groups
Jan Grebik
We show that every essentially countable orbit equivalence relation induced by a continuous action of a Polish group on a Polish space is -lacunary. In combination with [Invent.…
Borel selector for hypergraphons
Jan Grebik
We show that there is a Borel way of choosing a representative of a -uniform hypergraphon. This extends the result of Orbanz and Szegedy where this was shown for graphons.