ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 20(2) (2000) 231-242
DOI: 10.7151/dmgt.1122


Vladimír Lacko

Department of Geometry and Algebra
P.J. Safárik University
Jesenná 5, 041 54 Košice, Slovakia
e-mail: lackov@Koš


For the Traveling Salesman Problem (TSP) on Halin graphs with three types of cost functions: sum, bottleneck and balanced and with arbitrary real edge costs we compute in polynomial time the persistency partition EAll,ESome,ENone of the edge set E, where:

EAll = {e ∈ E,e belongs to all optimum solutions},
ENone = {e ∈ E,e does not belong to any optimum solution} and
ESome = {e ∈ E,e belongs to some but not to all optimum solutions}.

Keywords: persistency, traveling salesman problem, Halin graph, polynomial algorithm.

2000 Mathematics Subject Classification: 05C45, 68Q25.


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[7] V. Lacko, Persistency in the matroid product problem, in: Proc. CEEPUS Modern Applied Math. Workshop (AGH Kraków, 1999), 47-51.

Received 11 January 2000
Revised 29 March 2000