Three value TSP and linkages with the three value linear spanning 2-forests

Authors:
Daniel K. Benvenuti;Abraham P. Punnen
Affiliations:
-;-
Venue:
Discrete Applied Mathematics
Year:
2012

Citing 5
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Abstract

We provide a polynomially testable characterization of cost matrices associated with the complete directed graph where all disjoint spanning 2-paths (linear spanning 2-forests) have exactly one, two or three distinct values. Using this result, we identify a class of cost matrices where the number of distinct values of Hamiltonian cycles (paths) in a complete digraph is three. A complete characterization of general cost matrices with the property that all associated Hamiltonian cycles have at most k distinct values is an open question for k=3.