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Only Connect

The graph represents a salesman’s area of activity with the shops that the salesman must visit each day. What route around the shops has the minimum total distance?

Travelling Salesman

Stage: 3 Challenge Level: Challenge Level:1

Mathematicians have found no general criterion to test
whether a graph contains a Hamiltonian circuit or not. This is
unfortunate because there are many important questions in graph
theory which depend on the existence or non-existence of
Hamiltonian circuits.