Abstract
In 1968, L. Lovász conjectured that every connected, vertex-transitive graph had a Hamiltonian path. In this paper the following results are proved: (1) If a connected graph has a transitive nilpotent group acting on it, then the graph has a Hamiltonian path; (2) a connected, vertex-transitive graph with a prime power number of vertices has a Hamiltonian path.
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