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Euler & Hamilton Path and Circuits

Eulerian Path:

An Euler path is a path that uses every edge in a graph with no repeats. Being a path, it does not have to return to the starting vertex.

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If the path starts and ends at the same vertex, then it is called an Euler circuit.

image 134

Eulerian Circuit:

An Euler circuit is a circuit that uses every edge in a graph with no repeats. Being a circuit, it must start and end at the same vertex.

image 135

Hamiltonian Path:

A Hamiltonian path also visits every vertex once with no repeats, but does not have to start and end at the same vertex.

Hamiltonian Circuit:

A Hamiltonian circuit is a circuit that visits every vertex once with no repeats. Being a circuit, it must start and end at the same vertex.

image 136
image 137

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