Author

Bowen Li

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Preprint Sep 2026

A nearly linear bound for the Lov\'asz conjecture

The celebrated conjecture of Lov\'asz from 1969 asks whether every connected vertex-transitive graph has a Hamiltonian path. Buci\'c, Christoph, Pokrovskiy and Steiner recently proved that every such graph on $n$ vertices contains a cycle of length $n^{2/3-o(1)}$. In this paper, we improve this bound to $n^{1-o(1)}$. O...

Bo-Wen Li, Abhishek Methuku · 1 citation

Preprint Jul 2026

Long Directed Cycles in Vertex-Transitive Digraphs

The search for Hamiltonian cycles in vertex-transitive graphs and digraphs is a classical problem at the interface of graph theory and group theory. In the undirected setting, this goes back to the well-known conjectures of Lov\'asz and Thomassen concerning Hamiltonian paths and cycles in connected vertex-transitive gr...

Bowen Li, Abhishek Methuku · 0 citations