On the NP-completeness of the Slither Link Puzzle

For many of the widely played games and puzzles, their computational complexities have been analyzed. In this paper, we consider a sort of puzzle “Slither Link” and prove that the problem which determines whether or not a given instance of puzzle has any solutions is NP-complete, by using a polynomial time reduction from the Hamilton Path Problem with respect to restricted graphs. In addition we consider Another Solution Problem for the puzzle, the problem which determines, for a given instance and its solution, whether there is another solution for the instance. We provide a strategy to prove its NP-completeness.