In 1968, L. Lovfisz 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 grap
Nilpotent groups and transitive graphs
β Scribed by Norbert Seifter
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 610 KB
- Volume
- 45
- Category
- Article
- ISSN
- 0095-8956
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Let β« be a finite connected regular graph with vertex set V β«, and let G be a subgroup of its automorphism group Aut β«. Then β« is said to be G-locally primitiΒ¨e if, for each vertex β£ , the stabilizer G is primitive on the set of vertices adjacent to β£ β£. In this paper we assume that G is an almost s