In step 6 of the Christofides algorithm it is implicitly suggested that there is an invarient that the euler circuit can always be shortcutted to an hamilton circuit, what exactly assures us that? e.g (let u,v,w be vertices in the graph.) in the euler circuit, if vertex v has already been visited once, and is being revisited after visiting u and right before visiting w what makes the shortcut edge u-w to always exist?
Why shortcutting euler circuit creates a hamilton circuit in Christofides algorithm
algorithms;traveling salesman