Geodesic
On the~Number of Hamiltonian Cycles in Hamiltonian Dense Graphs
Matematičeskie trudy, Tome 8 (2005) no. 2, pp. 199-206.

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Let $G$ be a Hamiltonian graph with $n$ vertices and $Cn(n-1)/2$ edges, where $3/4$. We show that $G$ contains at least $(C_1n)^{C_2n}$ Hamiltonian cycles, where $C_1$ and $C_2$ are some constants depending on $C$, and prove an analog of Dirac's theorem for graphs with prescribed edges. 
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     author = {E. A. Okolnishnikova},
     title = {On {the~Number} of {Hamiltonian} {Cycles} in {Hamiltonian} {Dense} {Graphs}},
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E. A. Okolnishnikova. On the~Number of Hamiltonian Cycles in Hamiltonian Dense Graphs. Matematičeskie trudy, Tome 8 (2005) no. 2, pp. 199-206. http://geodesic.mathdoc.fr/item/MT_2005_8_2_a7/

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