Example 4.5.1.

Determine whether the graphs below have a Hamilton path.

The Petersen graph: ten vertices arranged in two rings of five each. Each outer vertex is adjacent to the two outer vertices closest to it, forming a pentagon, and to the inner vertex closest to it. Each inner vertex is adjacent to the two inner vertices not neighboring it, forming a 5-ponted star.
A graph with ten vertices. Five vertices form a copy of K5, the complete graph in which each vertex is adjacent to the other four. The remaining five vertices are each adjacent to only one of the five vertices in the copy of K5.
Solution.
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