Abstract
Circulant TSP is an intriguing special case of the Traveling Salesman Problem, whose complexity remains an often-cited open problem. In this note, we present three results: We show that circulant TSP can be efficiently solved whenever the input number of vertices is a prime-squared; we show that the {1,2}-TSP can be easily and efficiently solved when specialized to circulant instances; and we present a substantially-improved approximation factor for finding a minimum-cost Eulerian connected sub-(multi)graph on two-stripe circulant instances.
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