Mikhail Lavrov

activity

20152025

most citedAn upper bound for the Hales-Jewett number HJ(4,2)

1 citations · 2 across the 4 of their papers we have counts for

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9 papers · 1 filter

math.CO2025

Strong binding numbers and factors

Guantao Chen, Mikhail Lavrov, Yuying Ma +2

Let $G$ be a simple graph. The $k$ -th neighborhood of a vertex subset $S \subseteq V (G)$ , denoted $Λ^{k} (S)$ , is the set of vertices that are adjacent to at least $k$ vertices in $S$ …

math.CO2025

Bipartite graphs with the double Hall property

Guantao Chen, Mikhail Lavrov, Yuying Ma +2

The super-neighborhood of a vertex set $A$ in a graph $G$ , denoted by $Λ^{2} (A)$ , is the set of vertices adjacent to at least two vertices in $A$ . We say that a bipartite graph $G=(X…

math.CO2023

A Hall-type condition for path covers in bipartite graphs

Mikhail Lavrov, Jennifer Vandenbussche

Let $G$ be a bipartite graph with bipartition $(X, Y)$ . Inspired by a hypergraph problem, we seek an upper bound on the number of disjoint paths needed to cover all the vertices of…

math.CO2020

Conditions for a bigraph to be super-cyclic

Alexandr Kostochka, Mikhail Lavrov, Ruth Luo +1

A hypergraph $H$ is super-pancyclic if for each $A \subseteq V (H)$ with $∣ A ∣ \geq 3$ , $H$ contains a Berge cycle with base vertex set $A$ . We present two…

math.CO2020

Longest cycles in 3-connected hypergraphs and bipartite graphs

Alexandr Kostochka, Mikhail Lavrov, Ruth Luo +1

In the language of hypergraphs, our main result is a Dirac-type bound: we prove that every $3$ -connected hypergraph $H$ with $δ (H) \geq max {∣ V (H) ∣, \frac{∣ E ( H ) ∣ + 10}{4}}$ has a h…

math.CO2019★ 1 cited

Long monochromatic paths and cycles in 2-edge-colored multipartite graphs

József Balogh, Alexandr Kostochka, Mikhail Lavrov +1

We solve four similar problems: For every fixed $s$ and large $n$ , we describe all values of $n_{1}, \dots, n_{s}$ such that for every $2$ -edge-coloring of the complete $s$ -partite grap…