It says in the common mistakes when applying DP section:
If the longest path without repeated cities from city 1 to 2 pass through city 3, then the subpaths from 1 to 2 and from 2 to 3 may not be the longest paths without repeated cities.
What does it mean? Is this typo or correct?
If the path from c1 to c2 that is the longest passes thru c3, the subpath it uses for c1 to c3 is the longest path from c1 to c3 by definition. If there were any other subpath from c1 to c3 that was longer, that subpath would have been included in the longest path from c1 to c2.