Journal of Combinatorial Optimization

, Volume 30, Issue 3, pp 489–519

An extended approach for lifting clique tree inequalities


DOI: 10.1007/s10878-013-9647-3

Cite this article as:
Fischer, A. & Fischer, F. J Comb Optim (2015) 30: 489. doi:10.1007/s10878-013-9647-3


We present a new lifting approach for strengthening arbitrary clique tree inequalities that are known to be facet defining for the symmetric traveling salesman problem in order to get stronger valid inequalities for the symmetric quadratic traveling salesman problem (SQTSP). Applying this new approach to the subtour elimination constraints (SEC) leads to two new classes of facet defining inequalities of SQTSP. For the special case of the SEC with two nodes we derive all known conflicting edges inequalities for SQTSP. Furthermore we extend the presented approach to the asymmetric quadratic traveling salesman problem (AQTSP).


Traveling salesman problem Quadratic traveling salesman problem Polyhedral combinatorics 

Mathematical Subject Classification

90C57 90C27 

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsChemnitz University of TechnologyChemnitzGermany

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