[Math] Does the following graph have a Hamilton circuit

discrete mathematicsgraph theory

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A Hamilton circuit (or path) is a path that visits each vertex exactly once (except the start/end point) and ends at the starting point.

I've stared at this for quite a while and cannot find a Hamilton circuit yet my guide says that one exists. Where is the path?

Here's the lexicographically first Hamilton cycle (found using a backtracking algorithm):

A Hamilton cycle