Questions tagged [hamiltonian-circuit]

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Upper bound on the number of hamiltonian cycles on a $n \times n $ grid graph

What is the best upper bound that is known for the number of hamiltonian cycles on a $n \times n $ grid graph? I did some searching and found that the number of hamiltonian cycles on a planar graph ...
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Is Hamiltonian cycle problem on graphs with out-degree at most 3 NP hard?

I am trying to show a different form of Hamiltonian cycle problem is NP Hard. The problem is as follows. We have a directed graph and each node can have at most 3 outgoing edges. Determine if this ...
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Find reduction from Hamiltonian Cycle to Double Hamiltonian Cycle

$$DoubleHC=\{G\,| \text{G has at least two Hamiltonian Cycles}\}$$ I think about take a graph with HC and add to it two vertexes and edges to two randomally vertexes, but without success. Is my try ...