Abstract
In this paper, the tour problems in two-terminal series-parallel (TTSP) graphs is studied. A tour in a TTSP graph is a closed walk that passes a set of vertices. Those that pass every vertex at least once are called complete tour. The length of a tour is the summation of lengths of the edges in the tour. The shortest complete tour of a TTSP graph is a complete tour with minimum length. An O(¦E¦) time algorithm to find a shortest complete tour of a TTSP graph is presented, where ¦ E¦ is the number of edges in the graph. It is also shown that the bottleneck two-tour problem in a TTSP graph is NP-complete. The bottleneck two-tour problem in a TTSP graph is to find two tours such that each vertex of this TTSP graph must appear in exactly one of these two tours and the length of the longer tour of these two tours is minimized.
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