Mikhail Makarov

collaborators

3 papers

math.CO2026

Hamiltonian cycles and Hamiltonian paths in $2 k$ -connected, $1$ -tough and $(P_{3} \cup k P_{1})$ -free graphs

Hui Liu, Yingzhi Tian

A graph $G$ is called Hamiltonian if it possesses a Hamiltonian cycle; and $G$ is called Hamiltonian-connected if it contains a Hamiltonian path between any two distinct vertices.…

math.CO2026

Large induced forests in planar multigraphs

Mikhail Makarov

For a graph $G$ , denote by $a (G)$ the number of vertices in the largest induced forest in $G$ . The Albertson-Berman conjecture, which has been open since 1979, states that $a(G) \g…

math.CO2026

Branching $k$ -path vertex cover of forests

Mikhail Makarov

We define a set $P$ to be a branching $k$ -path vertex cover of an undirected forest $F$ if all leaves and isolated vertices (vertices of degree at most $1$ ) of $F$ belong to $P$ an…

Hamiltonian cycles and Hamiltonian paths in 2k-connected, 1-tough and (P3​∪kP1​)-free graphs

Large induced forests in planar multigraphs

Branching k-path vertex cover of forests

Hamiltonian cycles and Hamiltonian paths in $2 k$ -connected, $1$ -tough and $(P_{3} \cup k P_{1})$ -free graphs

Branching $k$ -path vertex cover of forests