I. Vorobyev

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math.CO2025

Weak saturation numbers of large complete bipartite graphs

Margarita Akhmejanova, Ilya Vorobyev, Maksim Zhukovskii

An $n$ -vertex graph $G$ is weakly $F$ -saturated if $G$ contains no copy of $F$ and there exists an ordering of all edges in $E (K_{n}) ∖ E (G)$ such that, when added one at a t…

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…

Weak saturation numbers of large complete bipartite graphs

Bicrucial k-power-free permutations

Bicrucial $k$ -power-free permutations