Does anyone know how many Hamiltonian paths of the Hoffman-Singleton graph there are, or how I might go about figuring that out?
2026-03-27 06:09:48.1774591788
Hamiltonian paths of the Hoffman-Singleton graph?
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So far as I know, the count is unknown. Why do you want it?
The Odd-4 graph is a 35-vertex valence-4 subgraph, and it has 1419264 undirected Hamiltonian cycles, and 328345920 undirected Hamiltonian paths. With more vertices and a higher valency, the number of paths will be much higher.