Abstract: We suggested a problem, proved that the problem is a NP-complete one and designed an algorithm to solve the problem in this paper. To prove the correctness of the algorithm, we creat a kind of linner order to align all the instance of the problem. Using the linner order we defined, we can prove the non-existence of the smallest graph which make our algorithm fail by constructing a smaller graph than the smallest one. It seems our algorithm is a polynomial one. So we would like to discuss with more people.
Key words: Algorithm, HC problem, NP complete problem, MSP problem
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