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The paper presents an O *(1.2312 n )-time and polynomial-space algorithm for the traveling salesman problem in an n-vertex graph with maximum degree 3. This improves the previous time bound for this problem. Our algorithm is a simple branch-and-search algorithm. The only branch rule is designed on a cut-circuit structure of a graph induced by unprocessed edges. To improve a time bound by a simple analysis on measure and conquer, we introduce an amortization scheme over the cut-circuit structure by defining the measure of an instance to be the sum of not only weights of vertices but also weights of connected components of the induced graph.

An Exact Algorithm for TSP in Degree-3 Graphs via Circuit Procedure and Amortization on Connectivity Structure