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When do we say that a test path ๐‘๐‘ tours a sub-path ๐‘ž๐‘ž with a side-trip?A test path ๐‘๐‘ tours a sub-path ๐‘ž๐‘ž with a side-trip when ๐‘๐‘ is an infeasible test path on its own.A test path ๐‘๐‘ tours a sub-path ๐‘ž๐‘ž with a side-trip when every vertex and every edge in q also occurs in ๐‘๐‘ in the same order.A test path ๐‘๐‘ tours a sub-path ๐‘ž๐‘ž with a side-trip when every vertex in ๐‘ž๐‘ž also occurs in ๐‘๐‘ in the same order.A test path ๐‘๐‘ tours a sub-path ๐‘ž๐‘ž with a side-trip when every edge in ๐‘ž๐‘ž also occurs in ๐‘๐‘ in the same order.

Question

When do we say that a test path ๐‘๐‘ tours a sub-path ๐‘ž๐‘ž with a side-trip?A test path ๐‘๐‘ tours a sub-path ๐‘ž๐‘ž with a side-trip when ๐‘๐‘ is an infeasible test path on its own.A test path ๐‘๐‘ tours a sub-path ๐‘ž๐‘ž with a side-trip when every vertex and every edge in q also occurs in ๐‘๐‘ in the same order.A test path ๐‘๐‘ tours a sub-path ๐‘ž๐‘ž with a side-trip when every vertex in ๐‘ž๐‘ž also occurs in ๐‘๐‘ in the same order.A test path ๐‘๐‘ tours a sub-path ๐‘ž๐‘ž with a side-trip when every edge in ๐‘ž๐‘ž also occurs in ๐‘๐‘ in the same order.

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Solution

We say that a test path ๐‘ tours a sub-path ๐‘ž with a side-trip when every vertex and every edge in ๐‘ž also occurs in ๐‘ in the same order. This means that the test path ๐‘ includes all elements of the sub-path ๐‘ž, but it may also include additional vertices and edges (the "side-trip"). The key point is that the sequence of vertices and edges in ๐‘ž must appear in ๐‘ in the same order.

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