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Number of labeled tournaments on n vertices with the maximum number of Hamiltonian paths.
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%I #11 Apr 29 2020 10:05:02

%S 1,2,2,24,64,480

%N Number of labeled tournaments on n vertices with the maximum number of Hamiltonian paths.

%C The maximum number of Hamiltonian paths in a tournament on n vertices is given by A038375.

%e For n = 4, the a(4) = 24 labeled tournaments with A038375(4) = 5 Hamiltonian paths are all isomorphic to the tournament on vertices {1,2,3,4} with edges {(1,2),(1,3),(2,3),(2,4),(3,4),(4,1)}, which have the following Hamiltonian paths:

%e 1->2->3->4,

%e 2->3->4->1,

%e 3->4->1->2,

%e 4->1->2->3, and

%e 2->4->1->3.

%Y Cf. A038375.

%K nonn,more

%O 1,2

%A _J. E. Paguyo_ and _Peter Kagey_, Apr 14 2020