Alexey Pokrovskiy

Bounded diameter monochromatic component covers

Abstract Ryser conjectured that every ‐edge‐coloured complete graph can be covered by monochromatic trees. Motivated by a question of Austin in analysis, Milićević predicted something stronger — that every ‐edge‐coloured complete graph can be covered by monochromatic trees of bou...

Hamiltonicity and structure of connected biclaw-free graphs

We show that for sufficiently large $d$, every balanced bipartite, connected biclaw-free graph with minimum degree $\geq d$ is Hamiltonian. This confirms a conjecture of Flandrin, Fouquet, and Li.