A Hamiltonian walk on a connected graph is a closed walk of minimal length which visits every vertex of a graph
(and may visit vertices and edges multiple times). For example, a Hamiltonian walk
on the above 3-pan graph is given by the vertex sequence
4, 3, 1, 2, 3, 4 and hence is of length 5.
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is called the Hamiltonian
number 
.
A Hamiltonian graph has 
, where 
is the vertex count. A
graph with 
is said to be almost Hamiltonian.
