GRAPH UTILITIES PACKAGE SYMBOL

FindHamiltonianCycle

FindHamiltonianCycle[g]
attempts to find a Hamiltonian cycle.

uses heuristic algorithms to find a Hamiltonian cycle, therefore, there is no guarantee that a Hamiltonian cycle will be found even if one exists.

This defines a small graph and finds a Hamiltonian cycle of the graph:

This plots the graph and highlights the cycle in red:

Needs["GraphUtilities`"]

This defines a small graph and finds a Hamiltonian cycle of the graph:

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This plots the graph and highlights the cycle in red:

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This limits the maximum number of iterations to try to find a Hamiltonian cycle:

This specifies a random seed different from the default to try to find a Hamiltonian cycle:

This finds all possible Hamiltonian cycles in the graph consisting of bordering countries in South America:

This shows the first of these two cycles; the second is just a reversal of the first:

uses heuristic algorithms. Unlike HamiltonianCycles, it is not guaranteed to find a Hamiltonian cycle even when one exists. But for large graphs,

can sometimes be faster at finding one cycle.

This defines a graph of 500 vertices, and uses these two functions to find a Hamiltonian cycle:

uses heuristic algorithms, which are not guaranteed to find a Hamiltonian cycle even when one exists: