Graph Theory

Hamiltonian Paths


Can you draw a path that visits every node exactly once (i.e. a Hamiltonian path) on the graph above?

Is there a Hamiltonian path on the complete graph Kn?K_n? (Note: the complete graph KnK_n is the graph with nn nodes where every pair of nodes has an edge between them.)

How many Hamiltonian paths are there on the graph above?

Does the graph above have a Hamiltonian path?

True or false: all Hamiltonian paths are Eulerian paths. (Note: an Eulerian path is one that uses every edge.)


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