Lecture Six Notes

Lecture six covers the basics of Euler cycles and Hamiltonian circuits and their variants. The fundamental theorem about Euler cycles, due to Euler (1732), is considered the first theorem of graph theory, and asserts that a graph has an Euler cycle if it is connected (up to isolated vertices), and if every vertex has even degree. Proof, and its variants, are straightforward, and are in the Tucker text.

The existence or non-existence of an Euler cycle is easy to determine: just look at the degrees of the vertices.

A Hamiltonian circuit is a circuit that visits every vertex exactly once, then returns to the starting vertex.

-- RobbieMoll - 26 Sep 2006