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Graph Theory

Any connected group of things can be represented as a graph: cities and roads, people and friendships, and more. Learn why an even number of people have an odd number of friends.

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 \(K_n?\) (Note: the complete graph \(K_n\) is the graph with \(n\) 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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