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08/28/2023
Borel versions of the Local Lemma and LOCAL algorithms for graphs of finite asymptotic separation index
Asymptotic separation index is a parameter that measures how easily a Bo...
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06/30/2023
Borel Vizing's Theorem for Graphs of Subexponential Growth
We show that every Borel graph G of subexponential growth has a Borel pr...
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03/09/2023
Fast algorithms for Vizing's theorem on bounded degree graphs
Vizing's theorem states that every graph G of maximum degree Δ can be pr...
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08/04/2022
Descriptive combinatorics and distributed algorithms
This is a draft of an article to appear in the October 2022 issue of the...
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09/27/2021
Counting colorings of triangle-free graphs
By a theorem of Johansson, every triangle-free graph G of maximum degree...
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07/12/2021
Coloring graphs with forbidden bipartite subgraphs
A conjecture of Alon, Krivelevich, and Sudakov states that, for any grap...
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02/17/2021
Probabilistic constructions in continuous combinatorics and a bridge to distributed algorithms
The probabilistic method is a technique for proving combinatorial existe...
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06/28/2020