Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
418483 | Discrete Applied Mathematics | 2012 | 15 Pages |
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 kk distinct values is an open question for k≥3k≥3.
► New sufficient conditions for three value TSP cost matrices. ► Complete characterization of one, two, and three value linear spanning 2-forests cost matrices. ► New TSP solvable cases.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Daniel K. Benvenuti, Abraham P. Punnen,