given Dict=(act, eat, sat, ...) make a long chain (no repeats) with 2-letter overlaps

given (a list of 3-letter words)
   Dict=(act, ATT, eat, sat, sit, cat, bat, dog, god, mat, tim, kim, ...)
The object is to make a long chain (no repeats) with 2-letter overlaps.
                               e.g. -- [cat, ate, tea, eat, ATT, ...]
What's a good approach (in Python)?
              in Mathematica, it's easy to find   THE Longest    chain?
                             is this a typical NP-complete problem?
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