Aiya Kuchukova

most citedColoring locally sparse graphs

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math.CO2026

Sampling Colorings with Fixed Color Class Sizes

Aiya Kuchukova, Will Perkins, Xavier Povill

In 1970 Hajnal and Szemerédi proved a conjecture of Erdös that for a graph with maximum degree $Δ$ , there exists an equitable $Δ + 1$ coloring; that is a coloring where color class s…

math.CO2024

Bicrucial $k$ -power-free permutations

Margarita Akhmejanova, Aiya Kuchukova, Alexandr Valyuzhenich +1

In this work, we prove that for every $k \geq 3$ there exist arbitrarily long bicrucial $k$ -power-free permutations. We also show that for every $k \geq 3$ there exist right-crucial…

math.CO2024★ 1 cited

Coloring locally sparse graphs

James Anderson, Abhishek Dhawan, Aiya Kuchukova

A graph $G$ is $k$ -locally sparse if for each vertex $v \in V (G)$ , the subgraph induced by its neighborhood contains at most $k$ edges. Alon, Krivelevich, and Sudakov showed that f…

Sampling Colorings with Fixed Color Class Sizes

Bicrucial k-power-free permutations

Coloring locally sparse graphs

Bicrucial $k$ -power-free permutations