# The complexity of restricted minimum spanning tree problems

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## Abstract

We examine the complexity of finding in a given finite metric the shortest spanning tree which satisfies a property P. Most problems discussed in the mathematical programming literature—including the minimum spanning tree problem, the matching problem matroid intersection, the travelling salesman problem, and many others—can be thus formulated. We study in particular *isomonphism* properties—those that are satisfied by at most one tree with a given number of nodes. We show that the complexity of these problems is captured by the rate of growth of a rather unexpected—and easy to calculate—parameter.

## Keywords

Travel Salesman Problem Travel Salesman Problem Hamilton Path Minimum Span Tree Problem Positive Cycle
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer-Verlag Berlin Heidelberg 1979